George  Davidson 

1  R9  £_T  Q1 T 


Pr.ofessor  of  Geography 
University  of  tTafifdrrfia 


• '   - 


'  "^•jS£  -^  *"1>4 ' 


IHE  STARRETT  BOOK 

for 
MACHINISTS'  APPRENTICES 


BY 

HOVARD  P.  FAIRFIELD 
i  * 

Assistant  Professor  Machine  Construction,  Worcester  Polytechnic  Institute 
AND 

CARL  S.  DOW,  S.  B. 

Editor-in-chief  Practical  Mechanical  Engineering 
Editor-in-chief  Practical  Shop  Work 


PRICE,  50  CENTS 


THE  L.  S.  STARRETT  COMPANY 

The  World's  Greatest  Toolmakers 
ATHOL,  MASSACHUSETTS 


COPYRIGHT  1917 
THE  L.  S.  STARRETT  COMPANY 


INTRODUCTION 

Laying  out  work  preliminary  to  machining  is  trans- 
ferring blue-print  instructions  on  to  the  metal.  While 
the  blue-print  gives  dimensions  accurately,  without  any 
great  precision  in  the  drawing  itself,  lines  laid  out  on 
the  metal  are  to  be  worked  to  and  must  therefore  be 
accurate.  No  one  can  consider  himself  a  skilled  machinist 
unless  he  can  lay  out  his  own  work  and,  when  called 
upon,  lay  out  work  for  the  less  experienced. 

To  become  skilled  in  laying  out  should  be  the  aim  of 
every  apprentice.  Possessing  this  skill  gives  more  op- 
portunity to  show  ability  than  the  running  of  a  machine. 
It  is  a  qualification  one  must  have  for  advanced  posi- 
tions such  as  toolmaker,  foreman,  or  superintendent. 

But  laying  out  requires  some  knowledge  of  mathe- 
matics, some  skill  at  mechanical  drawing,  and  an  acquaint- 
ance with  machinists'  fine  tools  and  shop  operations. 
Attention  to  details  and  extreme  care  are  of  utmost  im- 
portance. Increased  labor  cost,  as  well  as  material 
wasted  because  of  errors  in  laying  out,  are  the  penalties 
of  mistakes. 

The  apprentice,  then,  should  lose  no  opportunity  to 
make  himself  capable  of  laying  out  work.  Close  observa- 
tion of  pieces  laid  out  by  skilled  machinists  is  one  way 
of  becoming  acquainted  with  the  art.  The  fortunate 
apprentice  may  also  have  opportunity  to  observe  a 
skilled  machinist  while  laying  out  various  jobs. 

The  number  of  measuring  and  laying  out  tools  or 
instruments  now  purchasable  is  very  great  and  the  ap- 
prentice must  become  familiar  with  practically  all  of 
them.  He  must  know  what  he  can  accomplish  with  each 
so  that  he  will  instinctively  select  those  best  suited  to  the 
job  in  hand. 

M510983 


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Economy  of  time  in  laying  out  is  another  element  of 
success.  Time-saving  tools,  such  as  the  dial  test  indi- 
cator, quick-acting  micrometer,  and  combination  set, 
should  be  among  those  ready  for  use.  The  combination 
set,  for  instance,  combines  a  rule,  square,  miter,  protrac- 
tor, center  square,  depth  gage,  height  gage,  and  level.  The 
fewer  the  tools  used,  provided  the  ones  at  hand  are  really 
good  ones,  the  less  the  bench  will  be  littered  with  tools 
which  may  be  used  only  occasionally. 

The  tools  in  a  machinist's  tool-box  are  a  sure  indica- 
tion of  his  ability.  A  well-fitted  kit  of  fine  tools  helps 
him  hold  a  job  in  hard  times  and  is  one  of  the  best 
assets  a  man  can  have  when  applying  for  a  job.  The  pos- 
session of  many  fine  tools  indicates  a  love  for  accurate 
work,  freedom  from  the  borrowing  habit,  and  a  deter- 
mination to  do  work  which  will  demand  recognition. 
Next  to  having  a  complete  outfit  of  fine  tools  is  the  dis- 
position on  the  part  of  the  apprentice  to  add  the  best 
tools  as  rapidly  as  he  can  afford  them. 

In  preparing  this  book,  the  aim  has  been  to  select 
those  elementary  features  most  essential  to  the  advance- 
ment of  machinists'  apprentices  and  students  in  techni- 
cal and  manual  training  schools.  It  is  intended  to  give 
such  students  a  portion  of  the  instruction  ordinarily 
given  by  the  teacher  or  by  more  experienced  machinists. 
It  will  also  serve  as  a  reference  book  for  data  not  to 
be  memorized. 


THE        S    T    ARRETT        BOOK 


READING  WORKING  DRAWINGS 

Drawing  is  the  language  of  the  engineer,  designer, 
and  machinist.  Unless  a  machinist  can  at  least  read 
working  drawings  he  cannot  be  known  as  a  skilled  me- 
chanic. Certain  conventions  relating  to  views,  lines, 
scales,  sections,  and  other  representations,  are  what  make 
up  the  language  of  drawings,  and  the  correct  use  of 
these  is  readily  learned.  A  set  of  working  drawings 
consists  of 

GENERAL  DRAWING,  showing  the  entire  machine 
with  all  the  parts  located  in  their  proper  relation  to  one 
another.  This  drawing  is  usually  made  to  a  reduced 
scale;  for  example,  one-quarter  or  one-half  size;  it  is 
often  termed  the  Assembled  or  Assembly  Drawing. 

DETAIL  DRAWINGS  show  each  part  of  the  machine 
separately;  they  are  often  termed  "detail,"  or  "details." 
A  detail  drawing  should  be  supplied  with  complete  data 
for  constructing  the  part,  such  as  dimensions,  material 
used,  number  of  pieces,  operations  to  be  performed,  etc., 
and  should  consist  of  sufficient  views  to  be  easily  read. 
In  practice  some  firms  group  several  details  upon  a  single 
sheet  —  others  place  a  single  detail  upon  a  sheet. 

SECTIONAL  DRAWINGS  show  certain  assembled 
portions,  as  if  a  part  of  the  stock  had  been  sliced  away 
to  more  clearly  illustrate  the  interior  construction,  often 
termed  "sections."  Position  of  "section"  is  shown  by  a 
full  line  drawn  through  a  "view"  and  lettered  at  each  end. 

BOLT  AND  SCREW  LISTS.  On  these  are  tabulated 
all  bolts,  screws,  etc.,  which  are  common  to  the  stock- 
room, and  necessary  to  the  erecting  of  the  machine. 

MOTION  DIAGRAMS.  Instruction  is  sometimes  nec- 
essary concerning  the  relation  of  certain  centers  to  the 
motion  of  parts,  velocity  ratios,  and  direction  of  motion; 
therefore  where  a  machine  has  a  number  of  more  or  less 
complicated  motions,  motion  diagrams  are  provided. 


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VIEWS.  All  material  things  have  three  dimensions; 
length,  breadth,  and  thickness  or  height.  The  draftsman 
of  necessity  makes  use  of  some  method  of  projection  to 
get  his  various  views  on  a  flat  surface  on  which  only  two 
dimensions  can  be  shown  —  the  method  of  projection  in 
machine-shop  use  places  the  front  view  with  the  other 
views  grouped  around  in  the  order  of  their  names,  as 
top  view  above,  bottom  view  below,  etc.;  each  view  cen- 
tering on  either  a  horizontal  or  a  vertical  center  line. 

FULL    LINE 


DOTTED  1TINE 

CENTER    LINE 

DIMENSION    LINE 

SHADE   LINE 


LINES.  Full  lines  on  a  drawing  indicate  the  visible 
lines  or  edges  of  the  object.  Dotted  lines  indicate  hidden 
or  invisible  lines  and  edges.  Broken  lines,  made  up  of 
dots  and  dashes,  indicate  center  lines.  All  lay-outs 
should  start  from  center  lines. 

Dimension  lines  are  usually  full  lines  with  a  break 
in  the  line  for  dimension  figures  and  an  arrow  head  at 
each  end  to  indicate  the  surfaces  dimensioned.  Section 
lines  are  parallel  lines  drawn  across  a  surface  which  is 
represented  as  being  in  section;  they  are  usually  drawn 
at  an  inclination  of  45°  or  60°,  and  equally  spaced. 
By  using  for  sections  various  combinations  of  full  and 
dotted  lines  and  special  spacings,  different  materials  of 
construction,  such  as  cast  iron,  steel,  etc.,  can  be  indicated. 

SCALES.  Where  convenient,  all  drawings  are  made 
actual  size,  termed  full  scale.  When  the  object  is  too 

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large  to  be  conveniently  represented  full  size,  the  draw- 
ing is  made  to  a  regularly  reduced  size,  called  a  reduced 
scale  drawing.  The  usual  scales  are  full-size,  half-size, 
quarter-size,  and  eighth-size,  also  known  as  12",  6",  3", 
and  IV2"  to  1  foot.  When  working  from  drawings  the 
dimension  figures  should  be  invariably  followed  —  meas- 
urements should  not  be  taken  from  the  drawing. 


BRASS  OR  BRONZE 


WHITE  ALLOYS 


ALUMINUM 


LEAD 


ZINC 


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ABBREVIATIONS.    All  information  on  a  drawing  is, 
when  possible,  abbreviated  as  follows: 

CONVENTIONAL  ABBREVIATIONS 


Finish:  Surface  is 
to  be  finished 

Scrape:   Surface 
is  to  be  hand- 
scraped 

R.  H.:    Right  Hand 

Grind:  Surface  is 
to  be  ground 

'  :    Feet 

L.  H.:    Left  Hand 

Face  :  To  square 
up 

"  :    Inches 

W.   L:     Wrought 
Iron 

Bore:  Use  of  bor- 
ing tools  or  bars 

Dia.  :     Diameter 

C.  I.  :    Cast  Iron 

Ream  :  Hole  should 
be  reamed 

Rad.  :    Radius 

M.  S.:    Machine 
Steel 
T.  S.:    Tool  Steel 
C.  R.  S.:    Cold 
Rolled  Steel 

Tap  :  Hole  is  to  be 
tapped 

Thd.:    Thread 

C.  S.  :  Carbon  Steel 
H.  S.  S.:    High 
Speed  Steel. 

Drill:  Hole  is  to 
be  drilled 

U.  S.  S.:   United 
States    Stand- 
ard 

Running  Fit,  Drive 
Fit,    Force    Fit, 
Shrink  Fit,  Taper 
Fit:   Allowances 
to    be    made    in 
size  of  shaft 

SCREW  THREADS,  STRUCTURAL  RIVETING,  PIPE 
FITTINGS,  LINE  SHAFT  BEARINGS,  etc.,  are  so  stand- 
ardized that  conventional  representations  are  always 
used  by  the  draftsmen. 


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MEASURING  TOOLS 

Measurements  in  general  are  those  of  length,  area, 
and  volume.  In  machine-shop  practice  the  measurement 
of  length  is  the  common  one.  This  is  of  such  impor- 
tance, and  many  of  the  measurements  are  of  such  exact- 
ness, that  a  multitude  of  measuring  tools  are  being 
marketed,  nearly  all  of  which  are  for  the  main  purpose 
of  obtaining  linear  measurements. 

THE  YARD.  In  the  United  States  the  Standard  of 
length  is  the  British  yard,  of  which  two  copies  are  owned 
by  the  United  States  Government. 

THE    METER,    which    is    the    French    standard    of 
length,  is  also  coming  into  use  in  the  United  States,— 
notably   in   instrument  work.     The   meter   equals   39.37 
inches. 

The  use  of  measuring  tools  in  machine  work  is 
largely  confined  to  the  thirty-sixth  subdivision  of  the 
yard,  or  the  inch.  The  inch  is  subdivided  into  various 
lengths,  of  which  the  ten-thousandth  part  is  the  short- 
est practical  shop  measurement.  Measurements  shorter 
than  this  are,  however,  common  enough  in  scientific 
laboratory  work. 

The  practical  machinist  and  toolmaker  divides  his 
work  into  two  classes : 

(a)  Flat  Work  and  (b)  Round  Work.  While  it  can- 
not be  said  that  each  class  has  its  distinctive  line  of 
measuring  tools,  the  workman  who  handles  flat  work 
only  will  usually  have  a  somewhat  different  set  of  meas- 
uring tools  from  the  workman  on  round  work. 

FLAT  WORK 

In  general  the  worker  on  flat  work  will  need  to  be 
provided  with  steel  rules,  dividers,  protractors,  straight 

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Combination  Set 


Toolmakers'  Calipers  Micrometer  Depth  Gage 

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edges,  steel  squares,  surface,  height,  depth,  and  thickness 
gages,  center  punches,  parallels,  slide  calipers,  etc. 

ROUND  WORK 

For  round  work  the  measurements  are  by  contact,  and 
the  usual  tools  are  those  having  contact  points.  Contact 
measurements  are  made  in  two  ways:  (a)  The  contact 
tool  is  first  set  to  some  standard  of  length,  as,  for  ex- 
ample, a  steel  rule,  or  a  standard  gage.  The  "set"  dimen- 
sion may  then  be  used  as  a  standard  for  testing  the  work. 
(b)  The  reverse  of  this  method  may  be  used  for  deter- 
mining sizes,  viz.:  by  first  setting  the  contact  points  to 
the  surfaces  of  the  work,  afterward  using  the  steel  rule 
or  standard  gage  to  read  the  size. 

"FEEL" 

The  accuracy  of  all 
contact  measurements  is 
dependent  upon  the  sense 
of  touch  (feel).  In  the 
case  of  skilled  workmen, 
as,  for  example,  toolmak- 
ers,  the  sense  of  touch  is 
highly  developed.  Using 
suitable  contact  measur- 
ing tools,  the  skilled  me- 
chanic can  readily  "feel" 
the  difference  in  contact 
made  by  changes  of  di- 
mensions as  small  as 
0.00025". 

In   the   human   hand 

the  sense  of  touch  is  most  prominent  in  the  finger-tips. 

Therefore  the  contact  measuring  tool  should  be  held  by 


15 


THE       STARRETT       BOOK 

the  fingers  only,  and  in  such  a  way  as  to  bring  it  in  con- 
tact with  the  finger-tips.  If  the  tool  is  harshly  grasped 
by  the  fingers,  the  sense  of  touch  or  feel  is  much  re- 
duced. For  this  reason  the  tool  should  be  delicately  and 
lightly  held  instead  of  gripped  tightly. 

The  more  common  tools  for  contact  measurements 
are  inside  and  outside  calipers,  used  in  conjunction  with 
steel  rules,  plug  and  ring  gages,  and  dimension  blocks. 

While  it  is  possible  to  transfer  by  "feel"  a  length 
with  an  error  not  exceeding  one-quarter  of  one  thou- 
sandth inch,  the  results  are  not  always  easily  read;  for 
this  reason  mechanics  prefer  to  use  direct  reading  tools 
for  the  more  accurate  contact  work.  Two  methods  of 
direct  reading  are  in  common  use. 


VERNIER  CALIPERS 

This  tool  is  a  combination  of  contact  points  and 
steel  rules.  One  of  the  contact  points  is  a  fixed  part 
of  a  graduated  steel  rule,  while  the  other  contact  point 
is  a  part  of  a  graduated  slider  mounted  upon  the  blade 
of  the  first.  By  combining  the  use  of  the  separate  scales, 
direct  readings  of  one-thousandth  part  of  an  inch  are 
readily  made. 


FRONT 


16 


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VERNIER  HEIGHT  GAGE 


^•^-*~" 

'1 


Another  adaptation  of  the  vernier  is  the 
height  gage.  By  means  of  the  vernier  it  is 
easy  to  make  readings  as  minute  as  one 
thousandth  part  of  an  inch.  This  instru- 
ment is  used  chiefly  where  close,  accurate 
measurements  of  height  must  be  obtained; 
the  method  of  using  is  clearly  shown  on 
page  105  where  it  is  used  in  finding  the 
center  to  center  distance  of  a  pair  of  jig 
buttons. 

By  means  of  suitable  adjustments,  one 
of  which  is  shown  on  the  accompanying 
illustration,  its  use  is  extended  to  include 
making  accurate  measurements  of  depth. 
The  tool  is  thus  rendered  particularly  de- 
sirable for  use  in  jig-making  for  the  depth 
of  a  recess  inside  the  jig  frame  may  be  read- 
ily obtained.  The  removable  jaw  allows  the 
user  to  make  reverse  measurements  on  the 
jig  frame. 


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MICROMETER  CALIPERS 

With  the  invention  of  the  micrometer  screw  there 
came  into  use  a  new  method  of  direct  readings  in  contact 
measurements.  The  great  accuracy  of  the  micrometer 
screw  becomes  evident  when  it  is  realized  that  threaded 
spindles  with  a  limit  of  error  of  0.001"  in  one-foot 
lengths  are  commercially  possible.  In  micrometer  con- 
struction with  a  used  length  of  screw  thread  of  one  inch 
only,  the  error  is  negligible.  A  micrometer  head  con- 
sists of  a  spindle,  threaded  forty  to  the  inch,  fitted 
through  a  threaded  sleeve,  having  an  enclosing  thimble 
fastened  to  its  outer  end.  Suitable  graduations  made 
axially  on  the  threaded  sleeve  combined  with  the  grad- 
uations on  the  edge  of  the  rotating  thimble  give  direct 
readings  of  one-thousandth  part  of  one  inch.  By  means 
of  a  vernier  scale  used  on  the  rear  of  the  sleeve  direct 
contact  readings  as  small  as  one  ten-thousandth  part  of 
one  inch  can  be  readily  made. 

Micrometer  screws  are  mounted  in  a  frame  which 
may  be  varied  in  shape  and  size  to  render  it  convenient 
for  the  desired  purposes.  The  contact  points  are  also 
shaped  to  the  particular  use  desired,  and  instruments  of 
this  type  in  a  variety  of  styles  and  of  the  highest  degree 
of  accuracy,  convenience,  and  finish  are  purchasable, 
for  either  inside  or  outside  measurements. 


For  measurement  by  thousandths  up  to  one-half  inch. 
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Micrometer  Measurements 

The  limit  of  accuracy  obtained  by  measuring  between  contacts  depends  on 
the  graduations  on  the  instrument.  It  is  evident  that  as  the  fineness  of  the 
graduation  increases,  the  chances  for  mistaking  one  graduation  for  another  also 
increase  so  that  some  other  method  of  determining  extremely  accurate  measure- 
ments must  be  devised. 

The  commpn  instrument  for  making  such  measurements  is  known  as  a 
micrometer-caliper.  It  combines  the  double  contact  of  the  slide  calipers  with 
a  screw  adjustment  which  may  be  read  with  great  accuracy. 

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HOW  TO  READ  A  MICROMETER 

The  pitch  of  the  screw  threads  on  the  concealed  part 
of  the  spindle  is  forty  to  an  inch.  One  complete  revolu- 
tion of  the  spindle,  therefore,  moves  it  lengthwise  one 
fortieth  (or  twenty-five  thousandths)  of  an  inch.  The 
sleeve  D  is  marked  with  forty  lines  to  the  inch,  corre- 
sponding to  the  number  of  threads  on  the  spindle. 

Each  vertical  line  indicates  a  distance  of  one-fortieth 
of  an  inch.  Every  fourth  line  is  made  longer  than  the 
others,  and  is  numbered  0,  1,  2,  3,  etc.  Each  numbered 


line  indicates  a  distance  of  four  times  one-fortieth  of 
an  inch,  or  one  tenth. 

The  beveled  edge  of  the  thimble  is  marked  in  twenty- 
five  divisions,  and  every  fifth  line  is  numbered,  from 
0  to  25.  Rotating  the  thimble  from  one  of  these  marks 
to  the  next  moves  the  spindle  longitudinally  one  twenty- 
fifth  of  twenty-five  thousandths,  or  one  thousandth  of 
an  inch.  Rotating  it  two  divisions  indicates  two  thou- 
sandths, etc.  Twenty-five  divisions  will  indicate  a  com- 
plete revolution,  .025  or  one-fortieth  of  an  inch. 

To  read  the  micrometer,  therefore,  multiply  the  num- 
ber of  vertical  divisions  visible  on  the  sleeve  by  twenty- 
five,  and  add  the  number  of  divisions  on  the  bevel  of 
the  thimble,  from  0  to  the  line  which  coincides  with  the 

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horizontal  line  on  the  sleeve.  For  example,  in  the  en- 
graving, there  are  seven  divisions  visible  on  the  sleeve. 
Multiply  this  number  by  twenty-five,  and  add  the  number 
of  divisions  shown  on  the  bevel  of  the  thimble,  3.  The 
micrometer  is  open  one  hundred  and  seventy-eight  thou- 
sandths. (7  X  25  =  175  and  175  +  3  =  178.) 

HOW  TO  READ  A  VERNIER 

Readings  in  ten  thousandths  of  an  inch  on  caliper 
squares,  micrometers,  etc.,  are  obtained  by  the  use  of 
a  Vernier,  named  from  Pierre  Vernier,  who  invented  the 
device  in  1631.  For  the  Vernier  caliper,  the  scale  on  the 
tool  is  graduated  in  fortieths  of  an  inch  (0.25).  On  the 
Vernier  plate  is  a  distance  divided  into  twenty-five  parts, 
and  these  twenty-five  divisions  occupy  the  same  distance 
as  twenty-four  divisions  on  the  scale.  The  difference 
between  one  of  the  twenty-five  spaces  and  one  of  the 
twenty-four  spaces  is  one  twenty-fifth  of  one-fortieth, 
or  one  thousandth  of  an  inch. 

To  read  the  tool,  note  how  many  inches,  tenths  (or 
.100),  and  fortieths  (or  .025)  the  0  mark  on  the  Vernier 


is  from  the  0  mark  on  the  scale;  then  note  the  number  of 
divisions  on  the  Vernier  from  0  to  a  line  which  exactly 
coincides  with  a  line  on  the  scale. 

In  the  engraving  above,  the  Vernier  has  been  moved 
to  the  right  one  and  four-tenths  and  one-fortieth  inches 


THE       STARRETT       BOOK 


(1.425"),  as  shown  on  the  scale,  and  the  eleventh  line 
on  the  Vernier  coincides  with  a  line  on  the  scale.  Eleven 
thousandths  of  an  inch  are,  therefore,  to  be  added  to 
the  reading  on  the  scale,  and  the  total  reading  is  one  and 
four  hundred  and  thirty-six  thousandths  inches  (1.436"), 
which  is  the  distance  the  jaws  have  been  opened. 

HOW  TO  READ  A  VERNIER  MICROMETER 

Readings  in  ten  thousandths  of  an  inch  are  obtained 
ON  THE  MICROMETER  by  the  use  of  a  Vernier,  which 
operates  on  the  same  principle  as  the  Vernier  on  the 
caliper.  In  this  case,  however,  ten  divisions  on  the  sleeve 
occupy  the  distance  of  nine  divisions  on  the  thimble. 
The  difference  between  the  width  of  one  of  the  ten 
spaces  and  one  of  the  nine  spaces  is  one-tenth  of  a 

THIMBLE 
LO  O 

JJ'I  J   I  I   I  I 


division  on  the  thimble.  Now  each  division  on  the 
thimble  represents  one-thousandth  of  an  inch,  and  one- 
tenth  of  one-thousandth  equals  One  ten-thousandth.  To 
read  a  ten-thousandth  micrometer,  first  note  the  thou- 
sandths as  in  the  ordinary  micrometer.  Then  observe 
the  line  on  the  sleeve  which  coincides  with  a  line  on  the 
thimble.  In  the  diagram  shown  above  there  are  nine 
vertical  divisions  visible  on  the  sleeve,  and  9  X  25  =  225, 
so  that  the  reading  of  the  ordinary  micrometer  would  be 
.225.  Line  marked  "7"  on  the  sleeve  coincides  with  a 
line  on  the  thimble  and,  therefore,  we  add  seven  to  the 
reading  of  the  ordinary  micrometer.  This  seven  is  seven 
ten-thousandths  (.0007),  and  the  readings  will  be  .2257. 


THE        STARRETT        BOOK 


JHHsflHiE 

h-r-izsl  ta^u.'V' 


'.062S 
i  3    .16 
\S  .312 
L/M7S 


Half-Inch  Micrometer 

For  measurement 
by  thousandths  up  to 
one-half  inch. 

The   anvil  is  shortened,   for 
use  in  places  where  the  ordinary 
anvil  is  too  long  to  be  inserted. 
Has    lock    nut    and    ratchet 
stop. 


Quick-Adjusting  Micrometer 
Has  ratchet  stop  and  lock  nut. 


Six-Inch  Micrometer 

For  measuring  round  work  to  4%   inches  and  flat 
work  to  6  inches. 


24 


THE       STARRETT       BOOK 


OPERATION  AND  ADJUSTMENT  OF  MICROMETERS 

QUICK  MEASUREMENTS.  A  micrometer  having  the 
quick-adjusting  feature  can  be  instantly  opened  or  closed 
to  any  size  within  its  capacity.  Pressure  of  the  finger 
on  the  end  of  the  plunger  allows  the  spindle  to  move 
instantly  to  the  desired  size  without  turning  the  thimble. 
When  the  finger  is  removed,  fine  adjustments  may  be 
made  in  the  usual  way. 

MICROMETER  AS  A  GAGE.  By  means  of  a  knurled 
lock  nut  the  spindle  can  be  firmly  fixed  in  position, 
making  the  micrometer  a  solid  gage.  Turning  the  lock 
nut  contracts  a  split  bushing  around  the  spindle,  keep- 
ing it  central  and  true. 

READJUSTMENT  FOR  WEAR.  When  slight  wear 
makes  correction  necessary,  the  readjustment  is  accom- 
plished by  various  means  depending  upon  the  kind  of 
micrometer.  With  the  Starrett  micrometer  the  anvil  is 
fixed,  not  movable,  and  correction  is  quickly  made  by 
inserting  a  spanner  wrench  and  turning  until  the  line  on 
the  sleeve  coincides  with  the  zero  on  the  thimble.  This 
feature  does  away  with  the  frequent  use  of  a  test  piece. 


25 


THE       STARRETT       BOOK 
TRANSFERRING  MEASUREMENTS 

Transferring  a  measurement  may  be  a  delicate  job 
or  not,  wholly  depending  upon  the  degree  of  accuracy 
sought.  The  most  common  of  all  machine-shop  tools 
for  transferring  measurements  are  steel  rules  and 
spring  calipers.  With  these  tools,  either  in  combination 
or  used  separately,  are  made  the  bulk  of  common  ma- 
chine-shop measurements,  whether  those  of  inside  or 
outside  surfaces. 


STEEL  RULES 

These  are  thin  blades  of  steel  of  varying  lengths, 
widths,  and  thicknesses,  usually  graduated  in  inches  and 
various  subdivisions  of  the  inch  upon  each  edge  of  both 
sides  and  often  at  the  ends.  The  makers  term  the  vari- 
ous subdivisions  of  the  inch  by  graduation  numbers, 
for  example,  No.  4  Graduation,  1st.  edge  64ths;  2d.  edge 
32ds;  3d.  edge  16ths;  4th.  edge  8ths.  By  means  of  slid- 
ing or  fixed  attachments  a  great  variety  of  length  meas- 
urements may  be  made  with  the  ordinary  steel  rule. 


SPRING  CALIPERS 

The  most  commonly  used  tool  for  contact  measure- 
ments is  the  ordinary  spring  caliper,  which  is  used  for 
measuring  over  surfaces  or  between  surfaces.  In-  shop 
language  this  is  called  making-outside-or-inside  meas- 
urements. The  legs  of  the  spring  caliper  are  curved 
down,  to  make  two  opposite  contact  points,  the  distance 
between  being  controlled  by  a  screw  which  works  against 
a  tension  spring.  For  either  outside  or  inside  measure- 
ments they  may  be  set  to  or  they  may  be  read  to  a 
graduated  steel  rule.  In  this  way  a  workman  can  trans- 
fer lengths  with  an  error  of  less  than  0.002".  Where 


THE        STARRETT       BOOK 

specially  accurate  spring  caliper  measurements  are  de- 
sired, fixed  gages  are  used  for  setting  the  contact  points. 
The  degree  of  accuracy  of  contact  is  dependent  upon 
what  the  workman  terms  "feel."  To  accurately  transfer 
a  dimension  with  spring  calipers  the  sense  of  "feel" 
must  be  well  developed  by  the  workman,  for  the  contact 
points  are  at  the  ends  of  very  slender  arms. 

Spring  calipers,  both  for  inside  and  outside  work, 
can  be  set  to  dimensions  either  larger  or  smaller  than 
the  gages  used  by  introducing  thickness  strips  between 
the  contact  points  and  the  over  or  inside  surfaces. 

Hard,  thin  tissue-paper  may  be  used  as  thickness 
strips,  or,  better  still,  steel  thickness  gages  or  "  feelers." 


Calipering  Over  a  Flange 
27 


THE       STARRETT       BOOK 


SPRING  DIVIDERS 

In  this  tool  the  contacts  are  points  at  the  ends  of 
straight  legs.  Dividers  are  used  for  measuring  dimen- 
sions between  lines  or  points,  for  transferring  lengths 
taken  direct  from  a  graduated  steel  rule,  or  for  scribing 


circles  or  arcs.  "  Feel "  does  not 
enter  to  such  an  extent  into  the 
transfer  of  dimensions  when  using 
spring  dividers  as  it  does  with 
spring  calipers;  however,  a  certain 
delicacy  of  touch  is  essential.  A 
magnifying  glass  is  a  wonderful 
help  for  the  accurate  transfer  of 
dimension  with  dividers.  If  a  con- 
siderable length  is  to  be  transferred, 
it  is  best  to  use  the  type  where  the 
points  are  adjustable  along  a  bar, 
known  as  a  Universal  Divider,  for 
the  points  do  not  then  incline  to 
the  surfaces  worked  upon. 


THE       STARRETT       BOOK 
FITS  AND  FITTING 

In  machine  construction  many  of  the  parts  bear 
such  a  close  and  important  relation  to  one  another, 
that  a  certain  amount  of  hand  fitting  is  essential  to  make 
the  surface  contacts  as  they  should  be.  If  the  surfaces 
in  contact  are  to  move  on  each  other  the  fit  is  classed 
as  a  sliding  or  running  fit.  If  the  surfaces  are  to  make 
contact  with  sufficient  firmness  to  hold  them  together 
under  ordinary  use,  the  fit  is  classed  either  as  a  driving, 
shrink,  or  forced  fit. 

SLIDING  FIT.  Under  this  head  may  be  classed  the 
litting  of  cross  and  traversing  slides  of  lathes,  milling 
machines,  drilling  machines,  boring  machines,  grinding 
machines,  and  planers.  In  most  of  these  fits  the  moving 
and  stationary  parts  are  held  in  contact  with  each  other 
by  means  of  adjustable  contact  strips  or  gibs,  sometimes 
known  as  packing  strips.  In  some  cases,  such  as  the 
tables  of  grinding  and  of  planing  machines,  their  weight 
keeps  them  in  sufficiently  close  contact. 

RUNNING  FITS.  The  journal  bearings  of  spindles, 
crank  shafts,  line  shafting,  etc.,  are  classed  under  this 
heading. 

FORGED  FITS  AND  SHRINK  FITS.  Under  this 
head  are  classed  those  fits  where  the  separate  parts  must 
become  in  use  as  if  they  were  a  single  piece;  as,  for 
example,  the  crank  pins  and  axles  in  locomotive  driving 
wheels,  the  cutter  heads  and  spindles  of  numerous  wood- 
working machines,  as  .well  as  many  other  cases. 

LIMITS.  In  the  case  of  running  and  of  sliding  bear- 
ings a  certain  amount  of  hand  fitting  is  necessary  to 
obtain  desired  results,  and  in  all  cases  certain  limiting 
requirements  obtain.  In  sliding  and  running  bearings 
the  limits  are  usually  those  of  alignment  and  of  contact, 
while  in  either  journal  bearings  or  in  flat  sliding  bear- 
ings it  is  essential  that  certain  accurate  contact  between 

29 


THE       STARRETT       BOOK 

the  surfaces  shall  be  made,  and  there  will  also  be  a  limit 
of  alignment  with  other  parts  of  the  machine.  For  ex- 
ample, in  the  engine  lathe  the  ways  or  vees  and  the 
cross  slide  of  the  tool  carriage  must  be  parallel  to  or 
at  right-angles  to  the  axis  of  the  spindles  within  set 
limits.  In  engine  lathe  construction  the  limit  set  for 
this  is  0.001"  in  a  foot  of  length.  In  testing  the  parts 
use  is  made  of  the  Universal  Test  Indicator  with  the 
needle  reading  on  a  dial  or  upon  a  sector  arm.  The 
indicator  may  be  clamped  to  a  test  bar,  a  straight  edge, 
or  direct  to  the  lathe  spindle;  also,  if  desired,  it  can  be 
and  often  is  held  upon  a  special  slider  stand  fitted  to 
the  vees  of  the  machine. 

In  the  making  of  shrinkage  and  forced  fits  the 
limits  are  usually  those  of  size.  The  amount  of  pressure 
necessary  to  place  the  two  parts  together  is  the  limiting 
fact  in  the  case  of  forced  fits.  In  forcing  the  axles  into 
locomotive  driving  wheels,  the  specifications  may  limit 
the  pressure  to  between  one  hundred  to  one  hundred 
and  fifty  tons.  However  specified,  it  in  fact  reduces  to 
limits  of  size  and  the  use  of  measuring  tools.  These  can 
be  of  the  direct  reading  contact  type,  as  the  micrometer 
and  vernier  bar,  or  of  the  indirect  reading  contact  type, 
as,  for  example,  the  ordinary  spring  caliper  used  in  con- 
junction with  thickness  gages  or  "feelers." 

AMOUNTS  TO  LEAVE.  Where  pins,  spindles,  etc., 
are  to  be  forced  irito  holes,  or  where  collars,  hubs, 
flanges,  and  other  machine  parts  are  to  be  shrunk  on  to 
spindles,  it  is  customary  to  make  the  diameter  allow- 
ance upon  the  spindle  rather  than  upon  the  hole.  The 
amount  which  it  is  necessary  to  add  to  the  spindle  or 
shaft  diameter  must  of  necessity  vary  with  the  length 
and  diameter  of  the  hole,  the  metals  used,  and  the  form 
of  the  surrounding  hub.  The  following  tables  give  cer- 
tain practice. 


30 


THE       STARRETT       BOOK 


Allowances  for  Different  Classes  of  Fits  —  Table  1 

(Newall  Engineering  Co.) 


Class 

Tolerances  in  Standard  Holes* 

Nominal 
Diameters 

Up  to  W 

%.M' 

!Vi6"-2" 

2yi«"-3" 

3*«M" 

4*«"-5» 

A 

High  Limit 
Low  Limit 
Tolerance 

+0.0002 
—0.0002 
0.0004 

+0.0005 
—00002 
0.0007 

+0.0007 
—0.0002 
0.0009 

+0.0010 
—0.0005 
0.0015 

+0.0010 
—0.0005 
0.0015 

+0.0010 
—0.0005 
0.0015 

B 

High  Limit 
Low  Limit 
Tolerance 

+0.0005 
—0.0005 
0.0010 

+0.0007 
—0.0005 
0.0012 

+0.0010 
—0.0005 
0.0015 

+0.0012 
—0.0007 
0.0019 

+0.0015 
—0.0007 
0.0022 

+0.0017 
—0.0007 
0.0024 

Allowances  for  Forced  Fits 


High  Limit 

+0.0010 

+0.0020 

+0.0040 

+0.0060 

+0.0080 

+0.0100 

F 

Low  Limit 

+0.0005 

+0.0015 

+0.0030 

+0.0045 

+0.0060 

+0.0080 

Tolerance 

0.0005 

0.0005 

0.0010 

0.0015 

0.0020 

0.0020 

Allowances  for  Driving  Fits 


High  Limit 

+0.0005 

+0.0010 

+0.0015 

+0.0025 

+0.0030 

+0.0035 

D 

Low  Limit 

+0.0002 

+0.0007 

+0.0010 

+0.0015 

+0.0020 

+0.0025 

Tolerance 

0.0003 

0.0003 

0.0005 

0.0010 

0.0010 

0.0010 

Allowances  for  Push  Fits 


High  Limit 

—0.0002 

—0.0002 

—0.0002 

—0.0005 

—0.0005 

—0.0005 

p 

Low  Limit 

—0.0007 

—0.0007 

—0.0007 

—0.0010 

—0.0010 

—0.0010 

Tolerance 

0.0005 

0.0005 

0.0005 

0.0005 

0.0005 

0.0005 

Allowances  for  Running  Fits  t 


X 

High  Limit 
Low  Limit 
Tolerance 

—0.0010 
—0.0020 
0.0010 

—0.0012 
—0.0027 
0.0015 

—0.0017 
—0.0035 
0.0018 

—0.0020 
—0.0042 
0.0022 

—0.0025 
-0.0050 
0.0025 

—0.0030 
—00057 
0.0027 

Y 

High  Limit 
Low  Limit 
Tolerance 

—0.0007 
—0.0012 
00005 

—0.0010 
—0.0020 
0.0010 

—00012 
—0.0025 
0.0013 

—0.0015 
—0.0030 
0.0015 

—0.0020 
—0.0035 
0.0015 

-0.0022 
—0.0040 
0.0018 

z 

High  Limit 
Low  Limit 
Tolerance 

—0.0005 
—0.0007 
0.0002 

—0.0007 
—0.0012 
0.0005 

—0.0007 
—0.0015 
0.0008 

—0.0010 
—0.0020 
0.0010 

—0.0010 
—0.0022 
0.0012 

—0.0012 
—0.0025 
0.0013 

*  Tolerance  is  provided  for  holes,  which  ordinary  standard  reamers  can  pro- 
duce, in  tw9  grades,  Classes  A  and  B,  the  selection  of  which  is  a  question  for  the 
user's  decision  and  dependent  upon  the  quality  of  the  work  required ;  some  prefer 
to  use  Class  A  as  working  limits  and  Class  B  as  inspection  limits. 

t  Running  fits,  which  are  the  most  commonly  required,  are  divided  into  three 
grades :  Class  X  for  engine  and  other  work  where  easy  fits  are  wanted ;  Class  Y 
for  high  speeds  and  good  average  machine  work ;  Class  Z  for  fine  tool  work. 

31 


THE       STARRETT       BOOK 
LIMITS  OF  TOLERANCE 

While  it  is  possible  to  produce  machine  parts  with 
measurements  refined  to  any  degree  of  accuracy,  ex- 
treme precision  may  prove  too  costly  for  commercial 
work. 

To  avoid  waste  of  time,  lahor,  and  money,  the  Taft- 
Peirce  Manufacturing  Company  has  formulated  a  set  of 
rules  which  defines  the  degree  of  accuracy  to  be  expected 
in  those  cases  where  specifications  and  drawings  do  not 
call  for  greater  precision  than  the  rules  provide  for. 

(1)  Full  information   regarding  limits   of  tolerance 
should  be  clearly  shown  by  drawings  submitted,  or  be 
definitely    covered    by   written    specifications    to    which 
reference  must  be  made  by  notations  on  the  drawings. 

(2)  Where  the  customer  fails  to  supply  proper  data 
as  to  limits,   this   Company's   Engineers   will   use   their 
best  judgment  in   deciding  just  what  limits  it  may  be 
advisable  to  work  to.     The  Company  will  not,  in   any 
event,  assume  responsibility  for  possible  excessive  cost 
brought   about   through   working   to   closer   limits   than 
may   be   necessary   nor   for  permitting  greater   latitude 
than  may  subsequently  be  found  to  be  proper. 

(3)  Where    dimensions    are    stated    in    vulgar   frac- 
tions with   no  limits   of  tolerance  specified,   it  will   be 
assumed  that  a  considerable  margin  for  variation  from 
figured   dimensions   is    available;     unless    otherwise    or- 
dered, the  Company's  Engineers  will  proceed  according 
to  the  dictates  of  their  best  judgment  as  to  what  limits 
should  be  taken. 

(4)  For   all   important   dimensions   Decimal   figures 
should  be  used  and  limits  clearly  stated  on  detail  draw- 
ings.    If  Decimal  figures  are  not  used  for  such  dimen- 
sions  a   notation    referring  to   the    degree   of   accuracy 
required  must  be  placed  prominently  on  the  drawing. 

(5)  It   is   frequently   necessary  to   reduce   fractions 

32 


THE       STARRETT       BOOK 

representing  fourths,  eighths,  sixteenths,  thirty-seconds, 
and  sixty-fourths  to  decimal  equivalents.  When  a  dimen- 
sion of  this  character  is  expressed  in  a  decimal  equivalent 
and  carried  out  to  three,  four,  or  five  places  and  limits 
are  not  specified  it  will  be  assumed  that  a  limit  of  plus 
or  minus  .0015  is  permissible  unless  otherwise  ordered. 

(6)  Where  dimensions  are  stated  in  decimal  figures 
derived  by  other  processes  than  those  explained  in  para- 
graph five,  but  with  limits  not  specified,  the  following 
variations  from  dimensions  stated  may  be  expected: 

Two  place  decimals         .005  plus  or  minus 
Three     "  "  .0015 

Four      "  "  .0005 

Five       "  "  .0002 

(7)  Where  close  dimensions,  such  as  the  location  of 
holes   from   center  to   center  in   jigs,   fixtures,   machine 
parts,  and  other  exact  work   of  like   character  are  re- 
quired, detail  drawings  should  be  prominently  marked 
"ACCURATE"  and  clear  instructions  be  given. 

(8)  The   dimensions   of   internal   cylindrical   gages, 
external  ring  gages,  snap  gages,  and  similar  work  speci- 
fied to  be  hardened,  ground,  and  lapped,  will  be  obtained 
as  accurately  as  the  best  mechanical  practice  applying 
to   commercial  work   of  the   particular   grade   specified 
will  permit. 

(9)  As  drilled  holes  vary  in  size  from  .002"  to  .015" 
(and  in  some  cases  even  more)  over  the  size  of  the  drill 
used,  those  which  require  to  be  made  accurately  to  defi- 
nitely specified  sizes  should  be  either  reamed,  ground,  or 
lapped,  and  detail   drawings  thereof  should  bear  nota- 
tions accordingly. 

(10)  U.  S.  Standard  form  of  thread  and  pitches  will 
be  used  for  *4 -inch  and  all  sizes  above.    A.  S.  M.  E.  Stand- 
ard will  be  used  for  numbered  sizes  below  ^4 -inch.     In 
the  absence  of  specifications  to  the  contrary,  U.  S.  Stand- 
ard form  of  thread  will  be  used  for  all  SPECIAL  sizes. 

33 


THE        STARRETT       BOOK 


THE       STARRETT       BOOK 
BENCH  WORK 

Bench  work  includes  laying  out,  chipping,  filing, 
polishing,  hand  reaming,  hand  tapping,  and  all  the  many 
shop  jobs  done  at  the  bench  or  in  a  vise. 

LAYING  OUT.  This  is  the  shop  term  which  includes 
the  placing  of  lines,  circles,  and  centers  upon  curved  or 
flat  surfaces  for  the  guidance  of  the  workman.  It  is  some- 
what analogous  to  mechanical  drawing.  It  differs  in  one 
important  respect,  however,  that  while  a  line  drawing 
is  seldom  scaled  and  therefore  exact  accuracy  of  spac- 
ing is  not  required;  in  laid  out  work,  the  lines,  circles, 
centers,  etc.,  are  to  be  followed  exactly.  All  lines,  cen- 
ters, etc.,  should  therefore  be  exactly  located  and  placed, 
and  all  scriber,  divider,  and  center  points  should,  while 
in  use,  be  exact  and  sharp.  Particular  care  must  be 
maintained  to  insure  fine  and  accurate  laying  out. 

PREPARING  THE  SURFACE.  If  work  of  no  special 
accuracy  is  desired,  carefully  rubbing  chalk,  or  white 
lead  mixed  with  turpentine,  upon  the  surface  of  the 
work  will  be  sufficient  as  a  coating.  For  fine  exact  lay- 
outs a  special  marking  solution  must  be  used.  The  one 
in  common  shop  use  is  a  mixture  of  one  ounce  copper 
sulphate  to  four  ounces  water.  A  little  nitric  acid  may 
with  advantage  be  added.  This  solution  applied  to  a 
cleaned  iron  or  steel  surface  gives  a  dull  coppered  sur- 
face, and  the  finest  line  scribed  upon  it  is  brilliantly 
visible. 

SCRIBING  LINES.  The  usual  scribing  points  are 
those  common  to  dividers,  hermaphrodite  calipers, 
scratch  awls,  scratch  gages,  surface  gages,  and  trammel 
points.  Combined  with  the  scribing  points,  may  be  used 
steel  rules,  bevel  protractors,  steel  squares,  steel  straight 
edges,  levels,  end  measuring  rods,  micrometer  or  vernier 
height  and  depth  gages,  and  the  various  center  punches. 
Ability  to  so  combine  and  make  use  of  the  various  tools 

35 


THE        STARRETT       BOOK 


THE        STARRETT       BOOK 

as  to  insure  accuracy  is  a  considerable  asset  to  the  lay- 
ing-out man. 


PROTRACTORS 

As  made  for  machine-shop  use  the  common  protrac- 
tor is  provided  with  attached  straight  edges,  and  can  be 
used  either  to  measure  or  to  lay  off  lines  at  an  angle  to 
each  other.  Measuring  the  angularity  of  two  or  more 
lines  with  a  protractor  is  termed  "reading  the  angles." 
As  oftentimes  its  use  is  determining  the  angle  made  by 
two  surfaces  (a  bevel),  the  tool  is  usually  termed  a  bevel 
protractor.  Protractors  for  common  shop  use  are  grad- 
uated to  degrees  through  a  length  of  circumference  of 
one  hundred  and  eighty  degrees.  An  attached  vernier 
enables  the  user  to  read  angles  to  one-twelfth  of  a  degree 
(five  minutes). 

LAYING  OUT  PLATE.    If  desirable  results  are  to  be 

37 


THE       STARRETT       BOOK 

obtained  in  laying  out  flat  work,  special  metal  plates 
upon  which  to  rest  the  work  and  the  tools  must  be  pro- 
vided. These  are  known  as  leveling,  surface,  or  laying- 
out  plates;  they  furnish  an  accurate  plane  surface  upon 
which  work  and  tools  may  be  placed.  The  size  of  these 
plates  varies  from  those  of  small  areas  used  in  laying  out 
small  jigs,  etc.,  to  those  for  large  pieces,  having  sides 
several  feet  in  length.  The  work  may  be  laid  directly 
upon  the  surface  of  the  plate  or  held  upon  leveling  strips 
or  blocks  placed  on  the  plate,  and  the  gages,  squares,  and 
other  tools  used  around  the  work.  In  other  cases  it  is 
convenient  to  clamp  the  work  to  knee  or  angle  irons, 
which  are  then  placed  upon  the  leveling  plate. 

CHIPPING 

Formerly  many  of  the  surfaces  of  machine  parts 
were  hand-chipped  and  filed  to  a  fit.  While  the  mechanic 
in  the  modern  shop  can  usually  find  methods  of  machin- 
ing most  of  the  surfaces  he  needs  to  fit  up,  there  are  still 
occasions  when  the  work  has  to  be  hand-chipped. 

TOOLS  USED.  The  common  chipping  tools  are  a 
hand  hammer  and  a  hand  chisel.  The  hand  hammer 
should  weigh  not  less  than  three-quarters  of  a  pound 
nor  over  two  pounds,  and  may  be  either  of  the  ball  peen 
or  flat  peen  type.  A  chipping  hammer  should  balance 
well  in  the  hand  when  fitted  to  a  handle  not  more  than 
sixteen  inches  long.  The  handle  near  where  it  enters 
the  hammer  should  be  thinned  and  worked  down  to  a 
shank  that  is  somewhat  flexible,  so  that  the  shock  to  the 
arm  and  hand  will  be  less.  The  face  of  a  good  chipping 
hammer  should  crown  slightly. 

Chipping  chisels,  ordinarily  termed  cold  chisels,  are 
of  various  sorts,  and  are  often  known  by  the  shape  of 
the  cutting  end;  for  example,  flat,  cape,  roundnose,  dia- 
mond, and  gouge  chisels.  The  steel  from  which  they  are 


THE       STARRETT       BOOK 


made  should  be  eighty  to  ninety  point  carbon,  of  octa- 
gon cross-section,  with  the  cutting  end  forged  to  the 
desired  shape,  well  packed  by  the  forge  hammer,  hard- 
ened, and  the  temper  drawn  to  a  medium  blue.  The 


hammer  end  of  the  chisel  should  be  forged  from  the 
octagon  to  a  reduced  round  but  not  hardened.  Flat- 
chipping  and  cape  chisels  should  be  ground  with  straight, 
symmetrical,  cutting  edges,  at  as  acute  an  angle  as  the 
nature  of  the  work  will  permit. 

39 


THE       STARRETT       BOOK 

In  hand  chipping  the  hammer  handle  should  be 
grasped  near  the  end  and  the  hammer  swung  free  from 
over  the  shoulder  with  an  easy  forearm  movement. 
Hold  the  chisel  loosely  in  the  hand  at  an  angle  with  the 
work  that  permits  an  even  chip  of  right  depth.  The 
vision  should  be  directed  to  the  cutting  edge  of  the 
chisel,  rather  than  at  the  end  struck  by  the  hammer. 
Avoid  gripping  hammer  or  chisel  tightly,  as  this  rapidly 
tires  the  hand  and  arm. 

In  shops  which  have  compressed  air,  use  is  made  of 
the  modern  pneumatic  chipping  hammer,  which  does 
remarkable  work  of  the  heavier  sorts. 

FILING 

The  file  is  essentially  a  finishing  tool,  and  in  skilled 
hands  surfaces  may  be  made  very  accurate  and  smooth. 

Files  are  designated  thus  (a)  by  their  length  —  this 
does  not  include  the  tang;  (b)  by  their  cross-section,  as, 
for  example,  square,  round,  half-round,  triangular,  flat, 
knife-edge,  etc.;  (c)  by  their  cut  —  single  or  double  cut; 
(d)  by  the  degree  of  coarseness. 

Files  for  some  purposes  are  made  tapered  in  their 
length,  and  for  other  uses  have  straight  sides.  The  de- 
grees of  coarseness  are  designated  by  the  following 
names  as  rough,  coarse,  bastard;  2d  —  cut,  smooth,  and 
dead  smooth;  extra  fine  files  are  designated  by  numbers, 
No.  00,  No.  0,  No.  1,  etc.,  to  No.  8.  The  degree  of  coarse- 
ness varies  with  the  length,  for  example,  an  8-inch  file 
second  cut  is  coarser  than  a  shorter  file  bastard  cut. 
This  confuses  the  user  somewhat,  unless  he  is  familiar 
with  practice. 

Single-cut  files  are  those  having  teeth  made  by  single 
parallel  cuts  across  the  face  at  an  angle  of  twenty-five 
degrees.  In  double-cut  files  the  teeth  are  made  by  break- 
ing up  the  single  cuts  into  points  by  a  second  cut  made 
at  an  angle  with  the  first. 

40 


THE       STARRETT       BOOK 

Rasp  files  are  those  having  teeth  made  by  a  punch. 
Used  for  hoofs,  wood,  etc. 


HEIGHT  OF  WORK.  This  must  of  necessity  vary 
with  the  height  of  the  worker.  A  common  rule  is  to  have 
it  the  height  of  the  worker's  elbow  as  he  stands  erect. 
For  very  light  free-hand  filing  the  work  may  be  much 
higher,  in  some  cases  the  height  of  the  shoulders. 

41 


THE        STARRETT       BOOK 

POSITION  OF  THE  HANDS.  If  the  worker  wishes 
to  avoid  tiring,  position  is  very  important;  position  also 
has  direct  bearing  upon  the  quality  and  quantity  of  the 
product.  The  worker  should  clasp  the  file  handle  with 
the  extended  thumb  on  top,  grasping  the  point  with  the 
fingers  and  thumb  of  the  remaining  hand  with  thumb 
on  top.  In  heavy  filing  the  point  of  the  file  may  be 
grasped  by  the  fingers  and  the  palm  of  the  hand  with 
the  palm  on  top. 

In  hand-filing  the  worker  should  train  his  hands, 
arms,  and  body  to  carry  the  file  across  the  work  with 
regular,  even,  and  controlled  strokes.  As  the  file  is  in 
no  sense  self-guided  the  worker  must  train  his  body  to 
regular  controlled  motions  if  he  is  to  do  effective  work. 

DRAW  FILING.  Used  to  set  the  grain  somewhat 
smoother  than  regular  cross-filing.  The  worker  should 
clasp  the  blade  of  file  near  its  ends  in  each  hand  and 
then  draw  the  file,  held  crosswise,  along  the  length  of 
the  work.  A  fine  grain  surface  results. 

TESTING  FLAT  FILING.  Flat  work  is  tested  by  the 
use  of  steel  straight  edges,  steel  squares,  bevel  protrac- 
tors, etc. 


THE       STARRETT       BOOK 


POLISHING 

Where  a  particularly  smooth  surface  is  necessary,  as, 
for  example,  journal  bearings,  or  where  brilliancy  of 
finish  is  desired,  the  surfaces  are  polished  with  some 
fine  abrasive.  For  ordinary  polishing  of  machine  parts, 
journals,  etc.,  common  grain  abrasive  is  used,  —  glued  to 
cloth  or  leather. 

Grain  abrasives  are  known  by  numbers,  as,  for  ex- 
ample, No.  100,  which  means  that  the  particles  are  of 
a  size  to  readily  pass  through  a  sieve  having  one  hundred 
meshes  to  the  linear  inch.  The  finer  sizes  are  often 
known  as  flours. 

GRADES  OF  EMERY 

The  numbers  representing  the  grades  of  emery  run 
from  8  to  120,  and  the  degree  of  smoothness  of  surface 
they  leave  may  be  compared  to  that  left  by  files  as  follows : 

8  and  10  represent  the  cut  of  a  wood  rasp. 
16         20  a  coarse  rough  file. 


30 
40 
60 
80 
100 


120F  and  FF 


an  ordinary  rough  file, 
a  bastard  file, 
a  second  cut-file, 
a  smooth  file, 
a  superfine  file, 
a  dead-smooth  file. 


SEVERING  METAL  WITH  HACK  SAWS 

Hack  saws  are  narrow,  thin  blades  of  hardened  steel 
with  teeth  cut  along  one  edge,  and  are  used  for  severing 
metal.  They  are  held  in  suitable  hand  or  power  frames, 
which  have  the  necessary  adjustments  for  holding  the 
blade  in  stiff  tension.  It  is  obvious  that  it  requires  care 
and  good  sense  in  using  a  hack-saw  blade  if  good  results 
are  expected. 

If  the  stock  to  be  cut  is  both  hard  and  thin,  particular 
care  is  required  to  avoid  injuring  the  blade. 


43 


THE        STARRETT       BOOK 

CUTTING  SPEED.  When  hack  sawing,  under  aver- 
age conditions  and  without  a  lubricant,  a  cutting  speed 
of  fifty  to  sixty  strokes  per  minute  should  be  main- 
tained. If  the  saw  is  used  in  a  power  machine,  and  the 
material  is  soft  steel,  a  cutting  speed  of  one  hundred 
strokes  per  minute  may  be  made,  using  a  suitable  lubri- 
cant. Unannealed  tool  steel  should  be  cut  under  the 
above  conditions  at  not  to  exceed  sixty  strokes  per 
minute. 

MOUNTING  THE  BLADE.  The  blade  when  mounted 
in  a  hand-frame  should  have  the  cutting-teeth  rake  for- 


NO.I45 

TAKES  8  IN.TOI2  IN. SAWS 


ward;  that  is  to  say,  the  saw  should  cut  on  the  for- 
ward stroke.  In  machine  cutting  this  is  usually  so,  but 
not  so  with  some  makes  of  machines.  The  cutting  stroke 
is  always  the  pressure  stroke,  and  the  return  stroke  is 
made  as  light  as  convenient  without  actually  lifting  the 
blade  from  its  work. 

The  blade  should  be  under  considerable  tension 
when  in  use.  It  must  be  held  in  the  plane  being  cut, 
and  all  tendency  to  bending  the  blade  avoided.  Suitable 
blades  and  frames  may  be  purchased  for  almost  every 
service,  and  the  user  should  consider  this  fact  if  com- 
mercially economical  results  are  desired. 


44 


THE        STARRETT       BOOK 


HACK  SAW  MACHINE 


Hack  saw  blades  used  in  cutting  up  bar  stock  or 
structural  shapes  are  much  more  efficient  in  a  machine  so 
designed  that  its  several  motions  and  adjustments  can  be 
properly  controlled.  Such  a  machine  is  as  sensitive  to 
the  operator  as  a  hand  frame. 

The  machine  shown  above  has  been  especially  de- 
signed to  efficiently  operate  hack  saw  blades.  The  base 
column  carries  the  working  parts  and  the  work-holding 
vise.  By  means  of  suitable  weights,  the  cutting  pressure 
upon  the  blade  may  be  regulated  according  to  the  material 
being  severed,  and  the  stroke  length  of  the  blade-carrying 
frame  can  be  adjusted  to  use  the  entire  blade  length,  no 
matter  what  diameter  of  bar  is  being  severed,  thus  getting 
the  full  efficient  service  from  each  blade. 

To  avoid  blade  breakage  through  careless  handling, 
a  safety  device  in  the  form  of  a  dash  pot  is  connected 
with  the  blade-carrying  frame  to  prevent  the  blade  from 
being  dropped  suddenly  upon  the  work.  The  blade-carry- 

45 


THE       STARRETT       BOOK 


ing  frame  is  raised  by  a  foot  lever  leaving  the  hands  free 
for  work  adjustments  and  measurements.  The  cutting 
lubricant  is  conveyed  to  the  blade  from  a  tank  in  the 
column  by  means  of  a  small  rotary  pump. 

What  Hack  Saw  to  Use 

No.  103  in  hand  frames,  to  cut  cast  steel,  cast  iron,  tool  steels  and  all  solid 
metals. 

No.  103B  in  hand  frames,  to  cut  cold  rolled  stock  and  soft  metals. 

No.  102  in  hand  frames,  to  cut  sheet  metal  and  tubing  16  to  18  gage. 

No.  253  in  hand  frames,  to  cut  sheets  and  tubing  thinner  than  18  gage. 

No.  112  for  heavy  hand  frame  work  and  light  power  machines,  on  tool  steels. 

No.  112B  for  light  power  machine  work  on  soft  steel,  and  heavy  hand  frame 
work. 

No.  114  for  general  work  in  medium  weight  power  machines. 

No.  115  on  electrical  conduit,  pipe,  brass  stock,  light  angle  and  channel  iron. 

No.  255  on  high  speed  machines  cutting  tool  steels. 

No.  255B  on  high  speed  machines  cutting  machinery  steel,  cast  iron,  etc. 

No.  262  for  cutting  angle  iron,  brass  stock  and  ornamental  iron  work. 

No.  254  for  heavy  high  speed  machines,  to  cut  tool  steel. 

No.  254B  for  heavy  high  speed  machines,  to  cut  cold  rolled  shafting  and 
machinery  steel. 

No.  259  for  cutting  iron  pipe,  light  structural  iron,  auto  frames,  etc. 

No-  256  for  extra  heavy  power  machines,  to  cut  tool  steel. 

No.  256B  for  extra  heavy  power  machines. 


46 


THE       STARRETT       ROOK 


DRILLING 

DRILLS.  A  drill  is  an  end-cutting  tool,  consisting 
usually  of  two  cutting  edges  set  at  an  angle  with  the 
axis.  The  more  common  types  of  drills  are  flat  —  flat- 
twisted  —  straight-fluted  —  spiral-fluted  —  and  gun-barrel. 
The  most  common,  and  for  most  purposes  the  most  effi- 
cient, type  is  the  spiral-fluted,  known  as  a  twist  drill. 

Twist  drills  are  made  with  two,  three,  or  four  cut- 
ting lips.  The  two-lip  drill  is  used  when  drilling  solid 
stock.  The  three  and  four  lip  drills  are  used  for  en- 
larging holes  previously  cored  or  drilled.  When  drilling 
solid  stock  with  a  two-lipped  drill,  the  point  of  the  drill 
controls  the  cutting  edges,  and  if  the  drill  is  correctly 
ground  the  resulting  hole  will  be  reasonably  round, 
straight,  and  the  size  of  the  drill.  When  a  drill  is  used 
for  enlarging  holes  already  made,  either  by  coring  or  by 
previous  drilling,  the  drill  is  guided  by  its  sides  and  a 
three  or  four  fluted  drill  will  give  better  results. 

FORM  OF  POINT.  In 
the  types  referred  to  all 
except  gun-barrel  drills 
are  cone-pointed  on  the 
cutting  end.  The  gun- 
barrel  drill,  used  when 
especially  straight,  round, 
and  true  holes  are  essen- 
tial, has  a  blunt  end  with 
a  single  cutting  lip. 

A  cone-pointed  drill  of  two  or  more  cutting  lips 
depends  for  its  efficient  working  upon  four  factors: 

(a)  All  the  cutting  lips  shall  have  the  same  inclina- 
tion to  the  axis  of  the  drill. 

(b)  Cutting  lips  should  be  of  exactly  equal  length. 

(c)  A  proper  lip  clearance  of  the  surface  back  of 
the  cutting  edges. 


FIG.  1 


47 


THE       STARRETT       ROOK 


FIG.  2 


(d)   A  correct  angle  of  lip  clearance. 
Figs.  1,  2,  and  3  show  the  result  of  careless  free-hand 
grinding.     Figs.   4   and   5  show  how  to  test  the  length 
of  the  cutting  lips,  also  their  inclination  to  the  axis. 

After  sharpening  a 
drill  free-hand,  use  the 
hand-feed  at  first  and  ob- 
serve (a)  the  chips  made 
by  the  cutting;  (b)  the 
size  of  the  hole.  If  the 
cutting  lips  are  shaped  to 
a  proper  clearance,  the 
chips  will  curl  as  they 
start  from  the  cutting 
edge;  but  if  the  cutting 
lips  lack  a  proper  clearance  the  resulting  chips  have  the 
appearance  of  being  ground  off  rather  than  freely  cut. 
If  the  cutting  lips  are  of  uneven  length  the  hole  will  be 
enlarged  over  the  diameter  of  the  drill.  Drillings  from 
cast  iron  should  look  as  in  Fig.  6,  and  those  from  steel 
as  in  Fig.  7,  if  the  drill  is  properly  sharpened. 

Free-hand  grinding 
results  are  usually  so  dis- 
appointing that  in  most 
machine  shops  the  drills 
are  sharpened  in  a  spe- 
cial drill-grinding  ma- 
chine. The  design  of  this 
machine  is  such,  that 
when  it  is  set  for  grind- 
ing any  size  of  drill  the 
cutting  lips  are  made  of 
equal  length  and  of  the  correct  form.  Fig.  8  shows  how 
the  cutting  lip  is  located  to  correctly  grind  the  edges. 

FEEDING  THE  DRILL.    To  get  the  best  results  from 
drills   and   drilling  machines,  the   drill   should   advance 


FIG.  3 


48 


THE        STARRETT       BOOK 

into  the  work  a  definitely  regulated  amount  for  each 
revolution.  The  distance  which  the  drill  advances  per 
revolution  is  termed  the  FEED,  and  must  be  adjusted 
to  suit  the  conditions  under  which  the  work  is  being 
performed.  Table  No.  2  gives  the  feeds  per  revolution 
recommended  by  one  manufacturer  of  drills.  They  are 
recommended  for  average  conditions;  they  can  be  greatly 
exceeded  under  some  conditions,  but  must  be  reduced 
for  others. 


FIG.  4  FIG.  5 

Feeding  the  drill  freehand,  if  skilfully  done,  may 
answer  in  certain  cases,  but  is  less  effective  than  power 
feeds,  except  for  small  wire  drills. 

DRILL  SPEED.  This  is  the  surface  or  peripheral 
speed  of  the  drill  in  feet  per  minute,  and  is  rated  at  the 
outer  diameter.  Under  average  conditions  the  peripheral 
speed  recommended  for  carbon  steel  drills  is  thirty  feet 

49 


THE        STARRETT       BOOK 


to  forty  feet,  and  for  high-speed  drills  seventy  feet  to 
one  hundred  feet.  Working  conditions  may  at  times 
cause  a  change  in  these  figures.  When  the  extreme  outer 
corners  of  the  cutting  edges  wear  rapidly  it  is  evidence 
of  too  high  a  surface  speed. 


FIG.  6 


FIG.  7 


Table  No.  3  gives  the  revolutions  per  minute  at 
which  to  run  drills  for  various  cutting  or  surface 
speeds.  For  example,  with  a  1-inch  drill  and  seventy 
feet  as  the  selected  cutting  speed,  read  across  from 
1-inch  in  the  left-hand  column  and  under  heading  70' 
find  267,  the  revolutions  per  minute. 


FIG.  8 
60 


THE        STARRETT       BOOK 


Speeds  and  Feeds  for  Drilling*  — Table  2 

High-Speed  Steel  Drills 


Size 
of 

Feed 

Bronze, 
Brass, 

OAA 

Cast 
Iron, 
An- 

Cast 
Iron, 

Mild 
Steel, 

Drop 

Mai. 
Iron, 

Tool 
Steel, 

Cast 
Steel, 

Drill 

ReCv. 

300 
Feet 

nealed, 
170 

Hard, 
80  Feet 

120 
Feet 

Feet 

90 
Feet 

60 
Feet 

40 
Feet 

Feet 

Inches 

Inches 

R.P.M. 

R.P.M. 

R.P.M. 

R.P.M. 

R.P.M. 

R.P.M. 

R.P.M. 

R.P.M. 

Vie 

0.003 

18300 

10370 

4880 

7320 

3660 

3490 

3660 

2440 

Vs 

0.004 

9150 

5185 

2440 

3660 

1830 

2745 

1830 

1220 

%e 

0.005 

6100 

3456 

1626 

2440 

1210 

1830 

1220 

807 

Vi 

0.006 

4575 

2593 

1220 

1830 

915 

1375 

915 

610 

H« 

0.007 

3660 

2074 

976 

1464 

732 

1138 

732 

490 

% 

0.008 

3050 

1728 

813 

1220 

610  • 

915 

610 

407 

0.009 

2614 

1482 

698 

1046 

522 

784 

522 

348 

0.010 

2287 

1296 

610 

915 

458 

636 

458 

305 

0.011 

1830 

1037 

488 

732 

366 

569 

366 

245 

0.012 

1525 

864 

407 

610 

305 

458 

305 

203 

% 

0.013 

1307 

741 

349 

523 

261 

392 

261 

174 

1 

0.014 

1143 

648 

305 

458 

229 

349  - 

229 

153 

0.016 

915 

519 

244 

366 

183 

275 

183 

122 

1V2 

0.016 

762 

432 

204 

305 

153 

212 

153 

102 

1% 

0.016 

654 

371 

175 

262 

131 

196 

131 

87 

2 

0.016 

571 

323 

153 

229 

115 

172 

115 

77 

Carbon  Steel  Drills 


Size 
of 
Drill 

Feed 
JK. 

Bronze, 
Brass, 
150 
Feet 

Cast 
Iron, 
An- 
nealed, 
85 

Cast 
Iron, 
Hard, 
40  Feet 

Mild 
Steel, 
60 
Feet 

Drop 
Forg., 
30 
Feet 

Mai. 
Iron, 
45 
Feet 

Tool 
Steel, 
30 
Feet 

Cast 
Steel, 
20 
Feet 

Feet 

Inches 

Inches 

R.P.M. 

R.P.M. 

R.P.M. 

R.P.M. 

R.P.M. 

R.P.M. 

R.P.M. 

R.P.M. 

•We 

0.003 

9150 

5185 

2440 

3660 

1830 

2745 

1830 

1220 

0.004 

4575 

2593 

1220 

1840 

915 

1375 

915 

610 

9ie 

0.005 

3050 

1728 

813 

1220 

610 

915 

610 

407 

V4 

0.006 

2287 

1296 

610 

915 

458 

636 

458 

305 

£ 

0.007 

1830 

1037 

488 

732 

366 

569 

366 

245 

% 

0.008 

1525 

864 

407 

610 

305 

458 

305 

203 

7Ae 

0.009 

1307 

741 

349 

523 

261 

392 

261 

174 

% 

0.010 

1143 

648 

305 

458 

229 

343 

229 

153 

% 

0.011 

915 

519 

244 

366 

183 

275 

183 

122 

K 

0.012 

762 

432 

204 

305 

153 

212 

153 

102 

% 

0.013 

654 

371 

175 

262 

131 

196 

131 

87 

1 

0.014 

571 

323 

153 

229 

115 

172 

115 

77 

ttt 

0.016 

458 

260 

122 

183 

92 

138 

92 

61 

m 

0.016 

381 

216 

102 

153 

77 

106 

77 

51 

1% 

0.016 

327 

186 

88 

131 

66 

98 

66 

44 

2 

0.016 

286 

162 

77 

115 

58 

86 

58 

39 

*  Copyright,  1911,  by  the  Henry  &  Wright  Mfg.  Co. 
51 


THE        STARRETT       BOOK 


The  Speed  of  Drills— Table  3 

A  feed  per  revolution  of  .004  to  .007  for  drills  M  inch  and  smaller,  and  from 
.007  to  .015  for  larger  is  about  all  that  should  be  required. 

This  feed  is  based  on  a  peripheral  speed  of  a  drill  equal  to : 

30  feet  per  minute  for  steel ;  35  feet  per  minute  for  iron ;  60  feet  per  minute 
for  brass. 

It  may  also  be  found  advisable  to  vary  the  speed  somewhat  according  as  the 
material  to  be  drilled  is  more  or  less  refractory. 

We  believe  that  these  speeds  should  not  be  exceeded  under  ordinary  cir- 
cumstances. 

Table  of  Cutting  Speeds 


Ft.  per 
Minute 

15' 

20' 

25' 

30' 

35' 

40' 

45' 

50' 

60' 

70' 

80' 

Diam. 

REVOLUTIONS   PER  MINUTE 

ttein. 

917. 

1223. 

1528. 

1834. 

2140. 

2445. 

2751. 

3057. 

3668. 

4280. 

4891. 

% 

459. 

611. 

764. 

917. 

1070. 

1222. 

1375. 

1528. 

1834. 

2139. 

2445. 

tt« 

306. 

408. 

509. 

611. 

713. 

815. 

917. 

1019. 

1222. 

1426. 

1630. 

ft 

229. 

306. 

382. 

458. 

535. 

611. 

688. 

764. 

917. 

1070. 

1222. 

ttj 

183. 

245. 

306. 

367. 

428. 

489. 

550. 

611. 

733. 

856. 

978. 

% 

153. 

204. 

255. 

306. 

357. 

408. 

458. 

509. 

611. 

713. 

815. 

7Ae 

131. 

175. 

218. 

262. 

306. 

349. 

393. 

437. 

524. 

611. 

699. 

M 

115. 

153. 

191. 

229. 

268. 

306. 

344. 

382. 

459. 

535. 

611. 

% 

91.8 

123. 

153. 

184. 

214. 

245. 

276. 

306. 

367. 

428. 

489. 

% 

76.3 

102. 

127. 

153. 

178. 

203. 

229. 

254. 

306. 

357. 

408. 

% 

65.5 

87.3 

109. 

131. 

153. 

175. 

196. 

219. 

262. 

306. 

349. 

l 

57.3 

76.4 

95.5 

115. 

134. 

153. 

172. 

191. 

229. 

267. 

306. 

H6 

51.0 

68.0 

85.0 

102. 

119. 

136. 

153. 

170. 

204. 

238. 

272. 

m 

45.8 

61.2 

76.3 

91.8 

107. 

123. 

137. 

153. 

183. 

214. 

245. 

1% 

41.7 

55.6 

69.5 

83.3 

97.2 

111. 

125. 

139. 

167. 

195. 

222. 

1% 

38.2 

50.8 

63.7 

76.3 

89.2 

102. 

115. 

127. 

153. 

178. 

204. 

1% 

35.0 

47.0 

58.8 

,70.5 

82.2 

93.9 

106. 

117. 

141. 

165. 

188. 

1% 

32.7 

43.6 

54.5 

65.5 

76.4 

87.3 

98.2 

109. 

131. 

153. 

175. 

1% 

30.6 

40.7 

50.9 

61.1 

71.3 

81.5 

91.9 

102. 

122. 

143. 

163. 

2 

28.7 

38.2 

47.8 

57.3 

66.9 

76.4 

86.0 

95.5 

115. 

134. 

153. 

2K 

25.4 

34.0 

42.4 

51.0 

59.4 

68.0 

76.2 

85.0 

102. 

119. 

136. 

2V2 

22.9 

30.6 

38.2 

45.8 

53.5 

61.2 

68.8 

76.3 

91.7 

107. 

122. 

2% 

20.8 

27.8 

34.7 

41.7 

48.6 

55.6 

62.5 

69.5 

83.4 

97.2 

111. 

3 

19/1 

25.5 

31.8 

38.2 

44.6 

51.0 

57.3 

63.7 

76.4 

89.1 

102. 

52 


THE       STARRETT       BOOK 

CUTTING  COMPOUNDS.  To  maintain  high  cutting 
speeds,  it  is  necessary  to  use  a  lubricant.  Those  recom- 
mended have  stood  the  test  of  service : 

For  hard  and  refractory  steel,  turpentine,  kerosene, 
or  soda  water. 

For  soft  steel  and  wrought  iron,  lard  oil,  or  soda 
water. 

For  brass,  paraffine  oil. 

For  aluminum,  turpentine,  kerosene,  or  soda  water. 

For  cast  iron,  a  jet  of  air  if  anything  is  used  —  usu- 
ally worked  dry. 

LAYING  OUT.  Locating  the  centers  for  drilled  holes 
upon  the  body  of  the  work  is  termed  "laying  out."  On 
the  smaller  jobs,  laying  out  and  drilling  are  usually  done 
by  the  workman.  Larger  amounts  of  work  warrant  a 
skilled  "layer  out." 

Laying  out  for  drilling  comes  under  two  heads,  viz. : 
APPROXIMATE  and  ACCURATE.  Unless  the  holes  when 
drilled  are  to  match  up  with  other  holes  or  with  fixed 
studs,  it  is  enough  if  the  center  is  laid  off  with  a  chalk 
pencil  and  a  steel  rule.  For  jig,  tool,  and  experimental 
work,  the  centers  must  be  accurately  laid  out  and  scribed 
upon  the  surface  of  the  work.  The  practice  is  to  scribe 
two  or  more  lines  which  intersect  at  the  exact  desired 
point  as  shown  in  Fig.  9.  Assume  that  the  link  is  to 


FIG.  9 
63 


THE       STARRETT       BOOK 

connect  two  studs.  Proceed  to  scribe  two  intersecting 
lines  upon  one  of  the  hubs,  as  shown  in  Fig.  9,  using  a 
combination  square  fitted  with  a  center  head.  At  the 
intersection  accurately  place  a  light  center-punch  in- 
dentation. Place  one  leg  of  a  spring  divider  with  its 
point  in  the  center  mark  and  adjust  the  other  leg  to  have 
its  point  touch  the  edge  line  of  the  hub  and  note  the 
concentricity  of  the  center.  If  correct,  close  dividers  to 
scribe  a  circle  the  diameter  of  the  required  drilled  hole, 
setting  the  points  by  the  scale  graduations  upon  a  steel 


FIG.  10 

rule.     Locate  light  center-punch  marks   on   the   scribed 
circle  as  shown  in  Fig.  10. 

When   the   work   is   laid    out   by   another   than   the 


FIG.  11 
54 


THE        STARRETT       BOOK 

driller,  a  second  circle,  having  a  slightly  greater  diameter, 
should  be  scribed.  This  check  will  show  whether  the 
hole  was  drilled  to  the  original  lay  out.  If  no  impor- 
tance is  attached  to  the  center  to  center  distance  of  the 
holes  proceed  as  before  with  the  second  hub.  Where 
the  center  to  center  distance  is  important,  set  the  points 
of  the  universal  dividers  to  the  center  length,  and  with 
the  point  A,  Fig.  11,  in  the  previously  located  center  mark 
scribe  on  the  opposite  hub.  Scribe  a  short  line  across 
its  face  afterward,  proceeding  as  before. 

For  all  accurate  work  use  the  automatic  center- 
punch,  Fig.  12,  and  for  heavy  work  the  machinists' 
center-punch,  shown  in  Fig.  13. 

PREPARING  THE  SURFACE.  For 
accurate  laying  out,  clean  the  machined 
surfaces  and  wet  the  portion  to  be 
worked  upon  with  the  copper  sulphate 
(blue  vitriol)  solution.,  When  dry,  the 
surface  will  distinctly  show  any  lines 
which  are  made  upon  it.  Chalk  well 
rubbed  into  the  surface  is  sufficient  for 
the  less  accurate  jobs. 

STARTING  THE  DRILL. 
After  laying  out  and  previous 
to  drilling,  greatly  enlarge  the 
center  holes  with  a  center- 
punch  to  assist  the  starting  of  SCRIBING  CIRCLES  WITH  DIVIDERS 
the  drill.  Start  the  hole  with 

drill  point  in  the  enlarged  center,  using  hand  feed  until 
a  reasonable  dimple  is  made  in  the  work.  Observe  if 
this  is  central  with  the  scribed  circle,  and  if  not  central 
use  center  gouge,  as  in  Fig.  14,  and  repeat  until  accurate. 

TO  DRAW  A  DRILL.  When  starting  a  drill  it  often 
has  a  tendency  to  slide  or  crowd  off  to  one  side.  Where 
it  is  essential  that  the  drilled  hole  coincide  or  center 
with  some  previously  scribed  circle  or  layout,  the  drill 

55 


THE       STARRETT       BOOK 


FIG.  12 


must  be  brought  back  into  the  correct  posi- 
tion. This  is  accomplished  by  the  use  of  a 
small  gouge-pointed  chisel,  sometimes  called 
a  center  chisel,  and  the  process  is  termed, 
"drawing  the  drill."  First,  note  toward  which 
side  of  the  small  dimple  left  by  the  drill-point 
it  is  necessary  to  shift  the  drill.  Then 
chisel  a  small  groove  in  that  side  of 
the  dimple. 

If  the  start  is  very  eccentric,  sev- 
eral chisel  grooves  may  be  necessary; 
whereas,  if  only  slightly  eccentric,  a 
mere  touch  of  the  chisel  will  often 
suffice.  It  is  readily  seen  that  the  drill 
is  made  to  cut  more  easily  where  the 
grooves  are,  and  therefore  the  natural 
resistance  of  the  opposite  side  pushes 
the  drill  toward  the  side  cut  by  the 
gouge-pointed  chisel.  Drill  drawing 
can  only  be  done  previous  to  reach- 
ing the  full  diameter  of  cut. 

HOLDING  THE  WORK.  Careless- 
ness in  holding  the  work  is  respon- 
sible for  many  drilling  accidents.  If 
no  special  holding  device  is  available, 
the  work  should  be  held  in  a  drilling 
vise,  clamped  directly  to  the  drilling- 
machine  table,  or  clamped  to  an  angle 
iron.  Fig.  15  illustrates  a  method  of 
holding  the  work  safely.  When  once 
the  work  is  clamped  in  position  on 
the  drilling-machine  table,  adjust  the 
table  to  center  the  located  hole  with 
the  drill  rather  than  reclamp  the  work. 

HOLDING  THE  DRILL.  In  Fig. 
16,  at  A,  the  drill  is  shown  held  di-  FIG.  13 

66 


THE       STARRETT       BOOK 


rectly  in  the  spindle.  This  is  a  good  method  if  several 
holes  of  the  same  diameter  are  to  be  drilled  at  a  single 
setting.  When  frequent  changing  of  the  drill  is  neces- 
sary, as  in  drilling  holes  of  numerous  sizes,  using  a 
single-spindle  machine,  some  form  of  quick-acting  collett 
chuck  should  be  used.  The  changes  can  then  be  made 
without  stopping  the  machine. 


FIG.  14 


DRILLING  FOR  REAMER.  When  it  is  essential  that 
the  holes  be  of  an  exact  standard  diameter,  it  is  cus- 
tomary to  use  a  drill  somewhat  smaller  than  the  given 
diameter,  and  afterward  ream  the  holes  to  standard  size. 
The  amount  left  for  reaming  depends  upon  whether  one 
or  two  reaming  operations  are  necessary,  and  whether  or 
not  the  reaming  is  to  be  done  directly  in  the  drilling 
machine.  If  the  drilling  is  done  through  jig  bushings 
and  the  holes  are  short  as  compared  to  their  diameter, 


H 


FIG.  15 
57 


THE        STARRETT       BOOK 


a  single  reaming  operation  will  often  suffice.  If  the  holes 
are  relatively  long,  the  drill  should  be  1/64"  to  1/32" 
smaller  than  the  finished  hole  diameter,  to  allow  for 
passing  a  machine  reamer  0.005"  small  through  the  hole 
which  is  afterward  hand-reamed.  This  method  gives 
results  as  accurate  as  any,  except  by  grinding,  and  is 
accepted  practice  for  good  work. 

DRILLING  FOR  TAPPING.  Where  a  full  thread 
depth  is  essential  the  hole  to  be  tapped  should  be  made 
with  a  drill  of  a  diameter  smaller  than  the  nominal 
diameter  of  the  bolt  by  an  amount  equal  to  double  the 
depth  of  the  thread.  In  practice  the  nearest  commercial 
size  of  drill  is  listed  for  drilling  tapped  holes. 


THE        STARRETT       BOOK 


Letter  Sizes  of  Drills  —  Table  4 


Diameter 

Decimals 

Diameter 

Decimals 

Inches 

of  1  Inch 

Inches 

of  1  Inch 

A  i%4 

.234 

N 

.302 

B 

.238 

0  %« 

.316 

C 

.242 

P   2V64 

'       .323 

D 

.246 

Q 

.332 

E  M 

.250 

R   1V32 

.339 

F 

.257 

s 

.348 

G 

.261 

T   23/64 

.358 

H    17/64 

.266 

U 

.368 

I 

.272 

V   */8 

.377 

J 

.277 

W2%4 

.386 

K  %2 

.281 

X 

.397 

L 

.290 

Y  i%2 

.404 

U    1%4 

.295 

Z 

.413 

Sizes  of  Tap  Drills  — Table  5 


Tap 
Diameter 

Threads 
per  Inch 

Drill  for 
V  Thread 

Drill  for  U.  S. 
Standards 

Drill  for 
Whitworth 

M 

16,  18,  20 

5/32    %2       M/64 

%6 

3/16 

%2 

16,  18,  20 

%6    13/64    13/64 

5/16 

16,  18 

7/32    15/64 

M 

15/64 

*%« 

16,  18 

1A     17/64 

H 

14,  16,  18 

M       %2        %2 

%2 

%2 

%2- 

14',  16,  18 

19/64    2V64    2V64 

7/16 

14,16 

21/64    ^32 

1VS2 

Hb 

15/32 

14,16 

2%4     H 

1A    • 

12,  13,  14 

Z/8      2%4    25/64 

13/32 

H 

9/16 

12,14 

%6    29/64 

7/16 

N 

10,  11,  12 

15/32       Y2          l/2 

l/2 

y2 

Hie 

11,12 

O/               Q/ 

V16       716 

K 

10,  11,  12 

19/32       ^       5/8 

« 

% 

18/16 

10 

2V32 

% 

9,10 

45/64   23/32 

28/32 

2%2 

15Ae 

9 

49/64 

1 

8 

13/1P 

27/32 

27/32 

See  also  pages  78,  176  and  177. 


THE        STARRETT       BOOK 

Handy  Equivalent  Tables 
Made  of  Spring  Steel 


NO. 

THE  L.S.STARRETT  CO. 

ATHOL. MASS. U.S.A. 

DECIMAL 
EQUIVALENTS 


H  3 


590 


THE  L.S.STARRETT  CO. 
ATHOL.  MASS  U.S.A. 

\  TAP  DRILLS      I; 

FOR 

MACHINE  SCREW  TAPS 


rOR  STEEL  WORK  USE 
AP  DRILLS  ONE  OR  TWO 
SIZES  LARGER  THAN.  UST 


jto  V 

N°-(i§i)591 

THE  L.S.  STARRETT  CO. 
ATHOL.  MASS.  U.S.  A. 

DRILL  SIZE 
f       TABLE     fP 

1  LETTER  SIZES  1 

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THE        STARRETT       BOOK 

SIZES  OF  TAP  DRILLS.  Because  of  the  large  num- 
ber of  screw  thread  standards  in  use,  many  tables  would 
be  required  to  cover  all  selections  of  tap  drills. 

The  sizes  of  tap  drill  for  all  pitches  of  V  threads  may 
be  found  by  the  following  formula. 

1.400 
Tap  drill  =  D  - 

T 

in  which  T  =  number  of  threads  per  inch 
D  =  dia.  of  tap  or  thread 

EXAMPLE.  —  What  diameter 
of  tap  drill  should  be  used  for  a 
%  X  10  tap? 

1.400 
Tap  drill  =  .75  -£ 


=  .75  - 


10 
.14 


NOTE.  For  U.  S.  Standard 
threads  use  same  formula,  but 
1.3  should  be  used  in  place  of 
1.4. 

FIG.  17  DRILLING    LARGE    HOLES. 

Twist  drills  are  sold,  ranging  in 

size  from  No.  80  wire  gage  to  four  inches  in  diameter. 
As  the  drill  increases  in  diameter  the  web  is  corre- 
spondingly thickened,  and  as  the  cutting  edges  at  the 
web  do  not  cut  as  effectively  as  they  do  outside  the  web 
thickness,  considerable  pressure  is  required  to  force  the 
larger  drills  into  the  work  at  an  efficient  cutting  feed. 
For  this  reason  many  workmen  first  drill  a  lead  hole, 
using  a  drill  whose  diameter  approximates  the  web  thick- 
ness of  the  larger  drill,  as  shown  in  Fig.  17.  A  lead  hole 
will  also  assist  in  centering  the  drill  upon  an  inclined 
surface.  However,  if  the  inclination  is  considerable  it 
is  necessary  to  butt  mill  or  hand  chip  a  spot  giving 


61 


THE       STARRETT       BOOK 

sufficient  surface  to  work  upon.  The  practice  of  some 
firms  is  to  use  in  place  of  a  single  large  drill  a  relatively 
smaller  one,  afterward  enlarging  the  hole  by  some  method 
of  counterboring  at  a  much  less  expense  for  tools  and 
at  as  rapid  a  production  rate  as  by  entire  drilling. 

BOLT  HOLES.  When  the  bolts  are  for  holding  pur- 
poses only  and  are  not  used  for  aligning  the  several 
pieces,  it  is  customary  to  drill  the  holes  through  which 
the  bolts  pass  somewhat  larger  than  the  bolt  diameters. 
This  allows  for  a  variation  in  the  bolt  sizes  and  for  in- 
accuracy in  locating  the  centers. 

DEEP  HOLE  DRILLING.  Under  this  name  may  be 
classed  the  drilling  of  holes  through  the  axes  of  spindles 
—  lathe,  milling-machine,  and  grinder  —  and  that  special 
line  of  drilling  known  as  gun-barrel  drilling.  While  for 
spindle  drilling  it  is  possible  to  use  ordinary  twist  drills 
with  extended  shanks,  it  is  customary  in  efficient  drilling 
of  this  sort  to  use  special  drills  designed  for  the  purpose. 
Fig.  18  shows  a  special  hollow  drill  often  used  for 
drilling  axial  holes  in  lathe  spindles,  and  Fig.  19  shows 
the  machine  with  the  drill  guides  in  working  position. 


FIG.  18 

In  all  cases  of  deep-hole  drilling  it  is  better  to  rotate 
the  work  rather  than  the  drill.  The  drill  must  be  started 
exactly  concentric  with  the  axis  of  the  machine.  For 
this  reason  a  starting-hole  the  exact  diameter  of  the  drill 
is  first  counterbored. 

COUNTERBORING.  There  are  many  cases  in  which 
it  is  desirable  to  enlarge  a  hole  throughout  a  portion  of 


THE        STARRETT       BOOK 


FIG.  19 


its  length.  If  a  drill  is  used  for  this  purpose  there  is 
no  certainty  that  the  two  diameters  will  be  concentric. 
The  practice  is  to  enlarge  the  already  drilled  hole  by 
using  a  cutting  tool  having  a  pilot  or  leader  to  guide  the 
cutting  edges.  This  tool  is  known  as  a  counterbore,  and 
its  use  is  termed  counterboring.  In  Fig.  20  are  shown  the 
tool  in  operation  and  its  purpose. 


THE        STARRE    T    T        BOOK 


THE       STARRETT       BOOK 
THE  LATHE 

CARE  OF  THE  LATHE.  The  engine  lathe  is  capable 
of  producing  the  largest  variety  of  product  of  any  of 
the  machine-tool  family.  Especial  attention  should  be 
given  to  applying  a  suitable  machine  oil  to  all  the  bear- 
ings, for  improper  lubrication  of  the  wearing  surfaces 
is  one  of  the  immediate  causes  of  excessive  wear.  A 
medium-size  flexible-bottom  squirt  can  is  best  for  this 
purpose,  and  oiling  should  be  frequent  on  those  bear- 
ings which  are  given  the  severest  service,  either  from 
excessive  pressure  or  from  high-speed  rubbing.  All  oil 
holes  should  be  kept  free  and  clean,  and  where  possible 
should  be  protected  from  entering  dirt.  Those  bearings, 
as,  for  example,  the  ways  upon  which  the  carriage  moves, 
which  by  construction  are  hard  to  protect  "from  dirt, 
should  be  frequently  cleaned  and  reoiled.  At  least  once 
a  week  the  lathe  should  receive  an  all-over  cleaning, 
and  the  bearings  should  be  washed  out  with  kerosene. 
A  plugged  oil  hole  prevents  the  proper  lubrication  of  the 
bearing. 

INDICATING  AND  ADJUSTING.  Upon  the  condi- 
tion of  the  centers,  rests  to  a  large  degree  the  accuracy 
of  the  work  produced.  After  attention  to  lubrication 
the  competent  workman  proceeds  to  prepare  and  test 
the  centers.  Remove  both  centers  and  after  cleaning 
them  and  the  tapered  holes  note  whether  they  return  to 
their  places  with  a  successful  fit.  The  "dead"  or  foot- 
stock  center  should  have  a  hardened  point  to  resist  wear. 
The  cone-points  of  the  centers  should  be  smooth  and  an 
exact  sixty  degrees.  The  centers  should  align  with  each 
other  in  the  vertical  and  horizontal  planes,  and  the  "live" 
or  head-stock  cone-point  should  rotate  truly  concentric 
with  its  axis. 

The  trial  and  error  method  of  adjusting  the  centers 
in  alignment  is  to  first  bring  the  cone-points  nearly  into 

65 


THE        STARRETT       BOOK 

contact,  and  by  adjusting  the  foot-stock  frame  upon  its 
cricket  bring  them  into  as  exact  truth  as  is  reasonably 
possible.  With  the  foot-stock  clamped  in  position  to 
receive  the  work,  surface  the  diameter  of  a  trial  piece 
for  a  length  sufficient  to  allow  testing  its  diameter  at 
several  places.  If  the  diameter  increases  or  decreases 
as  the  tool  passes  along  the  length  of  the  work,  readjust 
the  foot-stock  and  repeat  the  test  until  the  required 


UNIVERSAL  DIAL  TEST  INDICATOR 
FIG.  21 

degree  of  accuracy  is  obtained.  To  test  the  live  center 
for  concentricity,  place  in  the  tool-post  a  universal  test- 
indicator,  as  shown  in  Fig.  21,  with  the  feeler  in  touch 
with  the  cone-point.  Rotate  the  head-stock  spindle 
slowly  by  hand  and  note  the  dial.  If  the  dial  shows  an 
eccentricity  in  excess  of  the  allowed  limits  for  the  job 

66 


THE       STARRETT       BOOK 

to  be  done,  the  cone-point  should  be  machined  true.  In 
cases  where  it  is  customary  to  have  the  live  as  well  as 
the  dead  center  hardened,  the  cone-point  must  be  trued 
by  some  grinding  attachment,  as,  for  example,  a  tool-post 
grinding  fixture.  By  many  workmen  the  live  center  is 
left  unhardened,  and  can  be  trued  with  a  square  nose- 
cutting  tool,  and  afterward  lightly  filed  to  a  smooth  sur- 


FIG.  22 

face.     To   test   either   center   for   its   proper   cone-point 

angle  use  is  made  of  a  center  gage,  shown  in  Fig.  22. 

TEST   INDICATOR.     This   is   a  tool   for  indicating 

minute  contact  variations  upon  a  graduated  dial  or  upon 


67 


THE       STARRETT       BOOK 


Truing  Work  in  Chuck 


Truing  Jig  on  Face  Plate 


Indicator  Used  with  Surface  Gage  on  Bench  Plate 
68 


THE        STARRETT       BOOK 

a  graduated  arc.  The  graduations  are  usually  one  hun- 
dred in  a  complete  circle  with  an  easily  read  width  of 
spacing.  The  instrument  is  built  in  such  a  way  that  one 
of  these  spaces  represents  a  movement  of  the  contact- 
point  of  1/1000  inch. 

Various  mechanisms  are  employed  for  multiplying 
the  movement  of  the  contact-point,  all  of  which  are 
based  upon  a  combination  of  short  and  long  arm  levers. 

USE.    The  test-indicator  may  be  used  with  advantage 
in  any  of  the  common  machine  tools,  to  in- 
dicate eccentricity  in  the  lathe,  milling  ma- 
chine, or  grinding  machine;    to  indicate  uni- 
formity of  height  in  the  planer,  shaper,  boring 
machine,  or  milling  machine;   to  indicate  par- 
allelism,   and   to    test    for    alignment    in    any_ 
machine. 

WORK  CENTERS.  Most  turned  work  is 
done  upon  the  lathe  centers,  and  it  becomes 
necessary  to  provide  suitable  cavities  in  the 
work,  coned  to-  fit  the  cone-points.  This  is 
termed  "centering  the  work,"  and  consists  in 
first  locating  the  position  of  the  cavities  and 
afterward  drilling  and  reaming  them  to  form 
and  size.  Best  practice  in  this  respect  is  to  use 
a  combination  drill  and  center  reamer,  as  it 
insures  exact  concentricity  in  the  drilled  and 
reamed  hole. 

LOCATING  THE  CENTERS.    It  is  evident 
that  the  centers  should  be  so  located  that  the 
entire  diameter  of  the  turned  job  shall  finish 
to  size.    Beside  this,  efficient  turning  demands  HERMAPHRO- 
that  the  chip  taken  shall  be  of  practically  uni-       DITE 
ftfrm  depth  as  the  work  rotates  against  the    CALIPERS 
cutting  tool.    For  these  reasons  some  degree  of  accuracy 
in  centering  is  necessary.    Where  the  turned  job  is  made 
from  ordinary  black  bar  stock,  the  centers  may  be  located 


THE       STARRETT       BOOK 


LATHE  TOOLS 


1  LEFT-HAND  SIDE  TOOL 

2  RIGHT-HAND  SIDE  TOOL 

3  RIGHT-HAND  BENT  TOOL 


4  RIGHT-HAND  DIAMOND  POINT 

5  LEFT-HAND  DIAMOND  POINT 

6  ROUND-NOSE  TOOL 


7  CUTTING-OFF  TOOL 

8  THREADING  TOOL 

9  BENT  THREADING  TOOL 


10  ROUGHING  TOOL 

11  BORING  TOOL 

12  INSIDE  THREADING  TOOL 


70 


THE       STARRETT       BOOK 

by  scribing  lines  at  an  angle  across  the  ends,  using  a 
combination  square  with  a  center  head  and  the  provided 
scriber.  In  place  of  this  tool  a  hermaphrodite  caliper 
may  be  used  to  scribe  the  ends  of  the  stock.  The  center 
is  located  with  a  center-punch  at  the  intersection  of  the 
scribed  lines  and  the  concentricity  tested  by  spinning 
the  bar  upon  the  lathe  centers.  If  necessary,  the  center- 
punch  marks  are  shifted.  If  the  piece  is  bent  it  must, 
after  centering,  be  straightened  to  reasonable  truth.  For 
exact  turned  work  the  centers  should  afterward  be  lightly 
rereamed  to  correct  the  errors  in  their  alignment  due  to 
the  straightening  of  the  bar. 

When  the'  job  is  to  be  turned  from  a  forging,  it  is 
usual  to  roll  the  forging  on  straight  edges  and  scribe 
lines  across  the  ends,  using  a  surface  or  height  gage. 
In  such  cases  the  forging  is  so  located  with  reference  to 
the  straight  edges  as  to  give  a  fair  average  of  the  surface 
errors  due  to  forging.  It  is  also  usual  to  leave  a  greater 
excess  of  stock  for  finishing  purposes  upon  a  forging 
than  upon  rolled  bar  stock.  When  the  centers  are  well 
located  the  holes  may  be  drilled  under  a  drill-press  or 
in  a  hand-lathe,  as  convenient.  Where  much  bar  stock 
must  be  centered  a  special  self-locating  centering  machine 
is  often  used. 

LATHE  TOOLS.  A  set  of  tools  for  use  in  the  engine 
lathe  is  shown  in  the  chart  on  page  70.  While  in  com- 
mon shop  language  all  these  are  known  as  cutting  tools, 
technically  speaking,  many  of  them  separate  the  stock  in 
a  manner  that  is  analogous  to  crowding  off  the  metal 
rather  than  by  pure  cutting  action.  Cutting  in  its  proper 
sense  is  a  splitting  action,  and  a  properly  ground  and 
properly  set  cutting  tool  is  a  wedge  in  that  it  splits  off 
the  excess  stock.  Among  the  common  lathe  tools,  the 
side  tool  and  the  diamond-point  tool  are  the  best  exam- 
ples of  wedge  or  splitting  action. 

The  nose  of  a  cutting  tool  has  several  sides,  two  of 

71 


THE        STARRETT       BOOK 


which  come  together  at  some  angle  to  form  a  cutting 
edge.  The  angle  formed  by  these  surfaces  must  be  suffi- 
cient for  strength,  and  to  furnish  enough  metal  to  con- 
duct away  the  heat  generated  by  the  cutting  action.  For 
turning  ordinary  soft  steel  and  soft  gray  iron  an  angle 
of  sixty  degrees  is  good  practice.  For  harder  material^ 
the  angle  may  be  increased.  In  the  case  of  forged  lathe 
tools,  the  working  end  of  the  tool  is  forged  upon  the  end 
of  a  short  piece  of  square  or  rectangular  bar  stock.  The 
length  and  size  of  the  shank  of  the  forged  tool  depend 
upon  the  size  of  chip  and  the  machine  used. 

•RAKE.     The  angle  which  the  upper  side  of  the  tool 
makes  with  the  horizontal  is  termed  the  rake.     If  the 


CLEARANCE 


FIG.  23 


SIDE 
CLEARANCE 


slant  is  away  from  the  work  it  is  termed  front  rake;  if 
in  the  direction  of  the  axis  of  the  work,  it  is  termed  side 
rake.  A  cutting  tool  may  have  its  upper  face  forged  and 
ground  with  either  a  front  or  a  side  rake  or  a  combina- 
tion of  both.  (See  Fig.  23.) 

CLEARANCE.  By  clearance  is  meant  the  angle  which 
the  under  side  of  the  tool  makes  with  the  vertical.  As 
in  the  case  of  "rake"  the  clearance  directly  away  from 
the  axis  of  the  work  or  lathe  is  termed  front  clearance, 

72 


THE       STARRETT       BOOK 

that  along  the  axis  of  the  work  side  clearance.  With 
the  tool  in  cutting  position  the  clearances  must  be  in  any 
case  not  less  than  three  degrees,  and  in  most  cases  not 
more  than  ten  degrees. 

RIGHT-HAND  TOOLS.  These  are  tools  having  the 
rake,  clearances,  and  cutting  edges  formed  to  turn  or 
square  from  the  right  towards  the  left. 

LEFT-HAND  TOOLS.  When  the  rake,  clearances, 
and  cutting  edges  are  formed  to  cut  from  the  left  to  the 
right  the  tool  is  known  as  a  left-hand  tool. 

SETTING  THE  LATHE  TOOL.  It  is  very  important 
that  the  lathe  tool  be  properly  set  in  relation  to  the  axis 
of  the  work  and  the  direction  of  the  cut.  While  there 
are  exceptions,  notably  that  of  the  diamond  point,  lathe 
tools  are  usually  set  with  the  cutting  point  at  the  exact 
height  of  the  axis  of  the  lathe.  In  the  case  of  the  dia- 
mond point,  the  front  clearance  is  usually  forged  to 
fifteen  degrees  or  over.  It  is  necessary,  therefore,  to  set 
the  point  above  the  axis  height  to  obtain  a  working  clear- 
ance of  not  to  exceed  ten  degrees'.  Unless  the  cutting 
tool  has  a  bent  shank  it  is  usually  set  at  right-angles  to 
the  surface  of  the  work. 

GRINDING  LATHE  TOOLS.  Lathe  tools  made  from 
carbon  tool  steel  should  be  sharpened  by  grinding  upon 
a  wet  emery-grinder,  or  upon  an  ordinary  water-drip 
grindstone.  If  made  from  the  newer  high-speed  steel 
the  grinding  should  be  upon  a  dry  and  rather  coarse 
abrasive  wheel.  The  grinder  should  have  a  suitable 
work-rest  upon  which  to  support  the  tool  in  sharpening 
the  larger  tools,  or  for  resting  the  hands  in  the  case  of 
the  smaller  tools. 

For  purposes  of  safety,  the  work  rest  should  be  firmly 
and  securely  clamped  as  close  as  possible  to  the  used  face 
of  the  wheel.  The  grinding  may  be  done  upon  the  pe- 
riphery of  a  disk-wheel  or  upon  the  sides  of  a  cup-wheel, 
as  desired.  In  any  case  the  wheel  should  rotate  to  force 

73 


TtH    E        STARRETT       BOOK 

the  tool  upon  the  rest  rather  than  from  it,  and  should 
run  true  and  in  balance.  Efficient  cutting  depends  very 
largely  upon  the  correct  sharpening,  as  well  as  the  cor- 
rect setting  of  the  cutting  tool,  and  great  care  should  be 
taken  when  grinding  a  lathe  tool  to  have  the  several 
faces  true  and  making  correct  angles  with  each  other. 
The  manner  of  doing  this  is  a  pretty  good  index  of  the 
workman.  The  usual  lathe-cutting  tools  have  well-de- 


45V 


FIG.  24 

fined  cutting  edges,  and  the  angularity  of  the  surfaces 
which  meet  to  form  the  cutting  edge  can  often  be  meas- 
ured with  a  bevel  protractor,  and  in  the  case  of  a  sixty- 
degree  angle  the  center  gage  is  suitable.  This  tool  is 
also  used  to  test  the  angle  when  grinding  a  vee-pointed 
thread  tool,  as  illustrated  in  Fig.  24. 

TESTING  THE  CUTTING  ANGLES.  As  the  usual 
machine  construction  materials  are  not  excessively  hard, 
a  cutting  angle  of  not  far  from  sixty  degrees  may 
be  maintained  on  such  tools  as  the  side  tool  and  the 
diamond  point.  In  this  case  the  angle  can  be  tested  by 
use  of  the  usual  center  gage.  Where  cutting  angles  other 

74 


THE        STARRETT       BOOK 

than  60°   are  used,  also  for  testing  clearances,  the  uni- 
versal Bevel  Protractor  is  useful. 

TOOL  HOLDERS.  The  high  cost  of  the  materials 
used  for  modern  cutting  tools  has  resulted  in  the  mar- 
keting of  a  variety  of  holders  designed  to  hold  cutting 
points.  In  this  manner  a  large  number  of  relatively 
inexpensive  cutting  points  are  made  to  interchange  in 
a  single  shank  or  holder.  One  form  of  tool-holder  is 
made  to  hold  points  forged  in  the  regular  forms  shown 
in  the  chart,  page  70.  In  some  examples,  however,  the 
holders  are  made  to  carry  short  bits  broken  from  square 
bar  stock  and  afterward  sharpened  into  some  resem- 
blance to  the  true  forged  shape.  (See  Fig.  25.) 


FIG.  25 

MATERIALS  FOR  GUTTING  TOOLS.  These  are 
known  as  carbon  steel  (tool  steel),  high-speed  steel,  and 
a  new  product  of  the  electric  furnace  sold  under  the 
trade  name  of  "Stellite."  Carbon  steel,  or,  as  it  was 
formerly  termed,  "tool  steel,"  is  high  in  carbon,  eighty 
point  to  one  hundred  and  twenty-five  point,  and  when 
correctly  heated  and  afterward  plunged  in  cold  water, 
hardens  to  a  very  high  degree.  Unfortunately  for  high- 
speed cutting  the  hardness  is  drawn  at  a  comparatively 
low  heat,  and  care  must  obtain  not  to  overheat  or  blue  it. 

High-speed  steel  is  a  special  steel  having  its  com- 
position alloyed  with  tungsten  and  perhaps  vanadium 
or  molybdenum.  While  heat  treatment  does  not  give  it 
the  exceeding  hardness  of  tool  or  carbon  steel,  high- 

75 


THE       STARRETT       BOOK 

speed  steel  has  the  peculiar  property  of  retaining  its 
hardness  at  temperatures  considerably  in  excess  of  those 
which  readily  soften  tool  steel.  Tools  made  from  high- 
speed steel  are  used  at  speeds,  feeds,  and  cuts  which 
heat  the  tools  and  chips  to  a  dull  red. 

Stellite  is  a  new  cutting  material  composed  of  chro- 
mium, cobalt,  and  sometimes  tungsten.  It  is  cast  into 
form  and  cannot  be  forged.  Its  hardness  is  equal  to  the 
diamond,  and  under  favorable  conditions  marvelous  turn- 
ing may  be  done. 

MANDRELS.  Where  the  work  is  to  be  turned  true 
with  a  hole  through  it,  as,  for  example,  turned  pulleys, 
work-centers  must  be  provided  for  holding  it  on  the  lathe 
centers.  The  common  way  is  to  force  or  drive  into 
the  work-hole  a  bar  having  center  holes  in  its  ends.  This 
bar  should  be  classed  as  a  tool-room  tool,  and  is  properly 
known  as  a  mandrel,  although  often  called  an  arbor. 

A  standard  set  of  mandrels  varies  in  diameter  and  in 
length,  according  to  the  shop  conditions.  They  are 
made  of  either  tool  steel  hardened  and  ground  true  with 
the  centers,  or  from  soft  machinery  steel,  case-carbonized 
and  afterward  ground.  The  ends  for  a  short  distance 
are  reduced  in  diameter  and  provided  with  flats  for 
clamping  on  the  dog.  Mandrels  usually  taper  at  the  rate 
of  0.0005"  in  an  inch.  The  diameter  of  the  hole  fitted 
by  the  mandrel  is  stamped  upon  the  larger  end.  As  the 
quality  of  the  work  depends  upon  the  truth  of  the  man- 
drel it  should  be  tested  upon  dead  centers  with  a  test- 
indicator  before  being  used.  To  use,  drive  or  force  it  into 
place,  using  a  Mandrel  press  for  forcing  or  a  lead  hammer 
for  driving,  carefully  removing  dirt,  chips,  or  pieces  of 
lead  from  the  centers  before  placing  the  work  in  a  lathe. 
Lathe  drive  with  the  usual  lathe-dog  as  for  any  job  done 
on  the  centers.  Avoid  forcing  or  driving  the  mandrel 
into  a  hole  that  is  neither  round  nor  straight.  Also  avoid 
scoring  the  mandrel  with  the  cutting  tool. 

76 


THE        STARRETT       BOOK 

SCREW  THREAD  CUTTING.  A  screw  thread  is  a 
helical  groove  cut  or  formed  into  the  surface  of  a  bar, 
rod,  or  bolt,  or  inside  a  nut.  For  ordinary  machine 
screws,  bolts,  studs,  etc.,  the  threads  are  made  with 
special  tools  called  threading  dies.  These  are  screwed 
upon  the  bolt,  screw,  or  stud  to  be  threaded  by  rotating 
either  the  work  or  the  die.  Threading  dies  are  used 
both  by  hand  and  in  power-driven  machines. 

SCREW  THREADS.  There  are  numerous  screw- 
thread  standards  in  more  or  less  general  use.  The  so- 
called  United  States  standard  is  in  this  country  the  more 
generally  accepted  one,  and  is  therefore  illustrated  in 
Fig.  26  and  Table  6.  It  will  be  noted  that  in  addition 
to  a  definite  form  of  thread  cross-section  each  diameter 
has  a  specified  number  of  threads  per  inch  of  length. 
The  United  States  standard  thread,  when  sectioned,  shows 
a  truncated  sixty  degrees  triangle  with  the  space  and 
the  land  alike. 

PITCH     AND     LEAD. 

Pitch    in    a    thread    is    the  ;  j /WIDTH 

distance  measured  from  the  "^  OF  FLAT 

center    of    one    thread    to         ~T 
the   center  of  an   adjacent  DEPTH 
thread.    If  the  screw  thread  OF™P, 
is  a  single  helix,  the  lead  is 
equal  to  pitch.    If  the  helix 
is  double,  the  lead  is  double  FlG- 26 

the  pitch.  While  strictly  speaking  pitch  is  the  reciprocal 
of  the  number  of  threads  per  inch,  as,  for  example,  1/7" 
pitch  for  a  screw  thread  7  per  linear  inch,  shop  men 
speak  of  it  as  7  pitch,  written,  7  P. 

THREADING  IN  A  LATHE.  When  screw  threads 
are  cut  in  an  engine  lathe,  the  point  of  the  cutting  tool 
is  shaped  to  the  exact  form  of  the  spaces  between  threads. 
By  means  of  a  lead  screw  and  a  train  of  gearing  the  tool 
is  compelled  to  move  along  the  axis  of  the  work  at  a 

77 


THE       STARRETT       BOOK 


U.  S.  Standard  Screw  Threads  —  Table  6 


Diameter 

No.  of  Threads 
per  Inch  | 

Diameter  at 
Root  of  Thread 

Diameter  of 
Tap  Drill 

Area  in 
Sq.  Inches 

,  Dimensions  of  Nuts 
and  Bolt  Heads 

1 

h^ 

k  •->! 

H 

a 

H 

& 

Of 
Bolt 

At  Root 
of 
Thread 

M 

20 

0.185 

13/64 

0.049 

0.026 

H 

0.578 

0.707 

1A 

1A 

H« 

18 

0.240 

H 

0.076 

0.045 

19/32 

0.686 

0.840 

5A6 

19/64 

« 

16 

0.294 

5Ae 

0.110 

0.068 

Hie 

0.794 

0.972 

H 

H'32 

7A6 

14 

0.345 

2%4 

0.150 

0.093 

2%2 

0.902 

1.105 

%e 

25/64 

H 

13 

0.400 

27/64 

0.196 

0.126 

% 

1.011 

1.237 

H 

7Ae 

%e 

12 

0.454 

15/32 

0.248 

0.162 

3V32 

1.119 

1.370 

9Ae 

3V64 

H 

11 

0.507 

17/32 

0.307 

0.202 

!Vl6 

1.227 

1.502 

5/8 

17/32 

H 

10 

0.620 

4V64 

0.442 

0.302 

\\i 

1.444 

1.768 

% 

N 

8 

9 

0.731 

% 

0.601 

0.419 

17/16 

1.660 

2.033 

7/8 

23/32 

8 

0.838 

5%4 

0.785 

0.551 

1% 

1.877 

2.298 

1%6 

V/8 

7 

0.939 

3V32 

0.994 

0.694 

113/16 

2.093 

2.563 

V/8 

29/32 

1M 

7 

1.064 

1%3 

1.227 

0.893 

2 

2.310 

2.828 

1M 

1 

1H 

6 

1.158 

1%2 

1.485 

1.057 

23/16 

2.527 

3.093 

IN 

1%2 

1H 

6 

1.283 

1H&2 

1.767 

1.295 

2^ 

2.743 

3.358 

i^ 

13/16 

iff 

V/2 

1.389 

!27/64 

2.074 

1.515 

2%6 

2.960 

3.623 

1% 

1%2 

i% 

5 

1.490 

!17/32 

2.405 

1.746 

2M 

3.176 

3.889 

1% 

1^ 

V/8 

5 

1.615 

l»%a 

2.761 

2.051 

21%6 

3.393 

4.154 

IK 

1!%2 

2 

4M 

1.711 

14%4 

3.142 

2.302 

33^ 

3.609 

4.419 

2 

1%6 

2M 

4X2 

1.961 

2V64 

3.976 

3.023 

3^ 

4.043 

4.949 

2M 

Ik 

2^ 

4 

2.175 

2'  %4 

4.909 

3.719 

3% 

4.476 

5.479 

2^ 

1^46 

2% 

4 

2.425 

2«%4 

5.940 

4.620 

«i 

4.909 

6.010 

2M 

2^ 

3^ 

2.629 

2i%e 

7.069 

5.428 

4N 

5.342 

6.540 

3 

2%6 

3J€ 

3^ 

2.879 

2i%e 

8.296 

6.510 

5 

5.775 

7.070 

3M 

2^ 

33^ 

3^ 

3.100 

3iy64 

9.621 

7.548 

5^ 

6.208 

7.600 

VA 

2^6 

3% 

3 

3.317 

3^g 

11.045 

8.641 

5« 

6.641 

8.131 

VA 

2>i 

4 

3 

3.567 

3^ 

12.566 

9.963 

6H 

7.074 

8.661 

4 

3Vi6 

4^ 

2^ 

3.798 

32%2 

14.186 

11.340 

6>i 

7.508 

9.191 

4^ 

VA 

4^ 

VA 

4.028 

4%2 

15.904 

12.750 

6K 

7.941 

9.721 

4K 

3%6 

4% 

25/8 

4.255 

45A6 

17.721 

14.215 

7M 

8.374 

10.252 

4M 

3^ 

5 

V/2 

4.480 

49/16 

19.635 

15.760 

7% 

8.807 

10.782 

5 

3i3Ae 

5M 

2l/2 

4.730 

4*%6 

21.648 

17.570 

8 

9.240 

11.312 

53€ 

4 

5^ 

zy* 

4.953 

5%a 

23.758 

19.260 

8^ 

9.673 

11.842 

5^ 

4%6 

5^ 

2*/8 

5.203 

5%2 

25.967 

21.250 

8^ 

10.106 

12.373 

5^ 

4^ 

6 

21A 

5.423 

5J/i 

28.274 

23.090 

9.H 

10.539 

12.903 

6 

4%6 

COURTESY  OF  "  MACHINERY  " 

See  also  pages  55,  56, 168  and 

78 


THE        STARRETT       BOOK 

definite  rate  of  advance  as  the  work-  rotates.  As  the 
train  of  gears  usually  furnished  with  an  engine  lathe 
can  be  changed  to  give  different  rates  of  advance,  it  is 
in  this  manner  possible  to  cut  threads  of  a. large  variety 
of  pitches.  In  practice  a  set  of  several  gears  having  dif- 
ferent numbers  of  teeth  are  furnished  with  each  lathe. 
Those  furnished  will  usually  provide  for  cutting  all  the 
threads  within  the  usual  range  of  the  lathe  with  which 
they  come.  These  are  known  as  "change  gears,"  and 
their  use  is  obvious. 

SELECTING  CHANGE  GEARS.  Given  the  number 
of  threads  per  linear  inch  to  be  cut  and  the  number  of 
threads  per  linear  inch  of  the  lead  screw,  the  problem 
is  to  select  gears  giving  the  desired  ratio  of  cut  to  lead 
screw.  For  example,  it  is  desired  that  single  seven 
threads  per  linear  inch  shall  be  cut  upon  a  li/d-inch 
bolt,  and  it  is  found  by  scaling  that  the  lathe  lead  screw 
has  single  five  threads  per  linear  inch.  The  ratio  of  cut 
to  lead  screw  is  then  that  of  seven  to  five  (7/5).  The 
change  gears  selected  should,  therefore,  be  as  seven  is 
to  five.  If  both  members  of  a  fraction  are  multiplied 
by  the  same  number,  the  ratio  is  not  changed.  This 
allows  of  raising  the  fraction  to  suit  the  gears  which  are 

7        5        35 
in  the  set  furnished;    for  example,  -  X  -  =  — .    If  gears 

5        5        25 

having  thirty-five  teeth  and  twenty-five  teeth,  respec- 
tively, are  found  in  the  furnished  set,  the  selection  of 
these  gears  will  give,  when  rightly  placed,  the  desired 
tool  advance  for  cutting  seven  threads  per  linear  inch. 

The  directions  above  refer  to  the  most  simple  form 
of  lathe.  Various  lathe  manufacturers  have  introduced 
different  arrangements  of  the  gearing,  but  with  any  lathe 
the  above  procedure  will  give  correct  results  if  it  is  first 
determined  what  number  of  threads  per  inch  will  be 
cut  if  gears  of  the  same  number  of  teeth  are  placed  on 
spindle  stud  and  lead  screw.  This  number  called  the 

79 


THE       STARRETT       BOOK 


Lathe  Set  Up  for  Thread  Cutting 
Note  Thread  Stop  at  A 


80 


THE        STARRETT       BOOK 


"lathe  screw  constant"  should  then  be  considered  as 
being  the  number  of  teeth  on  the  lead  screw  gear  even 
though  it  is  not  the  actual  number. 

PLACING  THE  CHANGE  GEARS.  The  common 
engine  lathe  has  projecting  through  its  headstock  a  shaft 
known  as  the  "stud."  This  projects  a  sufficient  distance 


STUD 
GEAR 


COMPOUND 
GEAR 
OUT  OF 
MESH 


INTERNED 
GEAR 


SIMPLE  TRAIN  OF  GEARS  FOR  THREAD  CUTTING 
81 


THE       STARRETT       BOOK 

to  allow  of  mounting  gearing  and  usually  the  upper 
cone  for  the  feed  belt.  Gears  mounted  or  to  be  mounted 
upon  this  projecting  stud  are  termed  "stud  gears."  Those 
mounted  upon  the  projecting  end  of  the  lead  screw  are 
known  as  lead  gears.  When  the  number  of  threads  to  be 
cut  is  more  per  linear  inch  than  that  of  the  lead  screw, 
the  smaller  of  the  selected  gears  is  placed  upon  the 
"STUD"  and  the  larger  upon  the  lead  screw.  In  the 
example,  the  25-tooth  gear  would  be  placed  on  the  stud 
and  the  35-tooth  gear  on  the  lead  screw.  Reverse  the 
order  if  the  number  of  threads  per  linear  inch  is  less 
than  that  of  the  lead  screw.  The  number  of  teeth  in  the 
large  idler  gear  has  no  bearing  upon  the  results,  as  it 
simply  conveys  the  motion  of  the  upper  or  stud  gear  to 
the  lower  or  lead-screw  gear.  In  the  above  it  is  assumed 
that  the  stud  rotates  in  unison  with  the  lathe  spindle. 

COMPOUNDING  THE  GEARS.  As  a  means  of  en- 
larging the  range  of  threads  per  linear  inch  possible  to 
be  cut  with  any  set  of  change  gears,  most  lathes  are 
provided  with  an  adjustable  compound  auxiliary  stud 
which  is  provided  with  two  locked  gears  having  a  ratio 
each  to  the  other  of  two  to  one.  As  an  example  of  their 
use,  assume  that  a  gear  having  ninety  teeth  was  needed 
upon  the  lead  screw  to  cut  a  given  number  of  threads. 
If  the  set  of  gears  furnished  failed  to  provide  a  ninety 
gear,  but  did  provide  one  of  forty-five  teeth,  placing 
this  on  the  lead  screw  and  meshing  the  two  to  one  com- 
pound stud  into  the  train  completes  the  desired  ratio, 
and  advances  the  tool  as  if  the  90-tooth  gear  had  been 
used. 

THREAD  TOOL.  Among  the  tools  listed  on  page  70 
is  shown  the  ordinary  threading-tool  point.  It  is  obvious 
that  this  or  any  other  form  of  point  must  be  formed  and 
tested  to  give  the  correct  form  of  thread.  The  point 
shown  has  sides  at  an  angle  with  each  other  of  sixty 
degrees.  The  point  can  therefore  be  tested  with  a  center 

82 


THE        STARRETT       BOOK 


STUD 
GEAR 


INTERMEDI 
GEAR 


COMPOUND  GEARS  FOR  THREAD  CUTTING 

gage  or  rule.  The  same  gage  may  also  be  used  in  setting 
the  tool  square  with  the  axis  of  the  work  (see  page  74). 
GRINDING  THREAD  TOOLS.  It  is  important  that 
the  point  of  the  thread  tool  shall  conform  to  the  outline 
of  the  groove  between  the  adjacent  threads,  and  that 
the  surfaces  below  the  cutting  edge  properly  clear  the 
stock  being  cut.  When  grinding  a  thread  tool,  particu- 


83 


THE       STARRETT       BOOK 


lar  care  should  be  given  to  have  the  clearances  sufficient 
for  the  lead  of  the  thread. 

SETTING  THE  TOOL.  Set  the  tool  point  at  the 
exact  height  of  the  lathe  centers,  and  at  right-angles  to 
the  axis  of  the  lathe. 

USES  OF  CUTTING  LUBRICANT.  Use  lard  oil 
when  threading  steel,  wrought,  and  malleable  iron.  Cut 
the  cast  metals  dry. 


THREAD  CUTTING  TOOL  SET  AT  HEIGHT  OF  LATHE  CENTER 

RIGHT  AND  LEFT  THREADS.  A  right-hand  thread 
results  when  the  threading  tool  is  advanced  from  right 
to  left  as  it  cuts.  If  the  tool  when  cutting  advances 
from  left  to  right  the  resulting  screw  has  a  left-hand 
thread. 

MEASURING  AND  TESTING  SCREW  THREADS. 
For  ordinary  purposes  screw  threads  when  cut  are  fitted 
to  some  threaded  hole.  This  may  be  a  hardened  and 
ground  gage,  or  may  be  an  ordinary  threaded  nut, 
depending  upon  the  accuracy  of  the  work.  Where  the 
quality  of  the  work  demands  special-  accuracy,  or  where 

84 


THE        STARRETT       BOOK 


standard  threaded  gages  are  not  available,  the  thread 
is  tested  by  measurements  made  with  calipers.  If  the 
point  of  the  thread  tool  has  been  carefully  and  exactly 
formed  and  accurately  set  in  place,  measuring  the  diam- 
eter at  the  root  of  the  thread  may  give  sufficiently  accu- 


CALDPERS  FOR  TESTING  THREADS 

rate  results,  and  this  may  be  done  with  a  set  of  thin 
point  spring  calipers.  When  greater  accuracy  than  this 
is  required,  micrometers  having  special  thread-measur- 
ing points  are  resorted  tox  (see  Fig.  27).  In  all  this  it 
is  assumed  that  the  thread  tool  is  ground,  set,  and  oper- 
ated to  give  an  exact  thread  outline. 

MEASURING  LATHE  WORK.  Work  done  in  the 
engine  lathe  is  of  such  a  variety  that  a  considerable  list 
of  measuring  tools  may  be  needed  to  cover  all  cases. 
Ordinarily,  however,  the  diameter  measurements  can  be 

85 


THESTARRETT       BOOK 


made  with  spring  calipers,  micrometers,  or  some  of  the 
usual  bar  calipers.  Cylindrical  plug  and  ring  gages, 
as  well  as  limit  snap  gages,  are  also  used  for  diameter 
measurements,  and  many  of  these  may  be  used  in  meas- 
uring the  shorter  lengths.  For  the  longer  measurements 
of  length,  steel  rules  are  provided  with  or  without  sliders. 
The  more  accurate  measurements  are  usually  made  by 
using  a  micrometer. 


FIG.  27 

TAPER  TURNING.  Where  two  parts  are  to  fit  firmly 
together  when  in  use,  as,  for  example,  centers  into  lathe 
spindles,  and  it  it  desirable  to  have  them  easily  remov- 
able, what  are  known  as  taper-fits  are  used.  For  this 
purpose  several  rates  of  change  in  diameter  have  become 
standards.  Pages  87  and  88  give  the  more  common  stand- 
ards. The  Brown  &  Sharpe  Standard  is  in  general  use 
for  the  spindle  tapers  in  milling  machines.  The  Morse 
taper  is  the  one  commonly  used  for  all  drills  and  drill- 
ing machinery.  Either  of  these  may  be  used  for  the 
tapered  hole  in  lathe  spindles,  while  some  lathe  manu- 
facturers have  established  standards  of  their  own. 

86 


THE        STARRETT       BOOK 


T 

IT 

T 

i 

s     ' 

I 

1 

i 

H 

| 

ANY 

*  i 

1 

l^v 

1 

1 

s^ 

Brown  &  Sharpe  Taper  Shanks— Table  7 


COLLET 

OR  SPINDLE 


Taper  per  ft.  is  Yz  in.,  except  for  No.  10  shank,  where  the  taper  is  0.5161  in.  per  ft. 


Number  of 
Taper 


Diam 
End  o 


0.239 
0.299 
0.375 
0.385 
0.395 
0.402 
0.420 
0.523 
0.533 
0.539 
0.599 
0.635 
0.704 
0.720 
0.725 
0.767 
0.898 
0.917 
1.067 
1.077 
1.260 
1.289 
1.312 
1.498 
1.531 
1.797 
2.073 
2.344 
2.615 
2.885 
3.156 
3.427 


t"0_*i 

gc 

f  o 


11%2 

2T/322 

21%2 

1% 

2%6 

2%2 

2i  %2 


327/32 
3% 

4% 

4y4 
4iyi6 

48/4 

617/32 

71%2 

9%r 

108/882 


18 

2y8 

2% 

i2y32 

2%2 
23/10 

2%e 

27/86 
3% 


417/32 

4% 

4%° 
47/6 


615/ie 
6*%2 


9%2 

92y32 
ioy4 


o    -o 

1 

(5      C/5 


0.200 

0.250 

0.312 

0.312 

0.312 

0.350 

0.350 

0.450 

0.450 

0.450 

0.500 

0.500 

0.600 

0.600 

0.600 

0.600 

0.750 

0.750 

0.900 

0900 

1.0446 

1.0446 

1.0446 

1.250 

1.250 

1.500 

1.750 

2.000 

2.250 

2.500 

2.750 

3.000 


il 

2 

U4. 

iiyie 
1% 

2 

2% 
2% 

sy4 

27/^ 
3 

3%6 

4yf 


6%2 


6»/4 


9H 


w 


2i  %4 

3iy64 

218/32 


517/32 


8%2 
817/32 


Length 
Keywa 


H 


15/10 


Width  of 
Keyway 


0.135 
0.166 
0.197 
0.197 
0.197 
0.228 
0.228 
0.260 
0.260 
0.260 
0.291 
0.291 
0.322 
0.322 
0.322 
0322 
0.353 
0.353 
0.385 
0.385 
0.447 
0.447 
0.447 
0447 
0.447 
0.510 
0510 
0.572 
0.572 
0.635 


gth  of 
ngue 


27/So 
27/32 


83 

££ 

•*  o 

SH 


M 


%- 
& 
%« 


8/8 


Vl«! 

n« 


87 


THE       STARRETT       ROOK 


Morse  Standard  Taper  Shanks  — Table  8 


ANY 


r 

1 

i 

i 

i 

K 

i  "> 

1 

i  1 

f 

ft! 

SOCKET  OR 

SPINDLE 


^ 
^ 

|H 


!o  «w 

"S  w— 

P  3  rt 

IEI 


0.252 
0.369 
0.572 
0.778 
1.020 
1.475 
2.116 
2.750 


Dia.  at  End 
of  Socket 


0.356 
0.475 
0.700 
0.938 
1.231 
1.748 
2.494 
3.270 


4Vie 
5%e 


•U    QC 

^ 


2H32 

3Me 

3»/4 

4% 
6 


4^8 

5V4 


lOfc 


K 


4i%0 

7 

9% 


Length  o 
Keyway 


2% 


ou 

II 

JH° 


*>* 


Thickness 
of  Tongue 


% 


Width  of 
Keyway 


W 


0.160 
0.213 
0.260 
0.322 
0.478 
0.635 
0.760 
1.135 


11 


2%2 

2% 


.625 
.600 
.602 
.602 
.623 
.630 
.626 
.625 


Short  Shanks 


0.271 
0.388 
0.600 
0.816 
1062 
1.532 
2.201 
2.857 


0.356 
0.475 
0.700 
0.938 
1.231 
1.748 
2.494 
3.270 


!5/8 

1% 
2? 

34* 

4^8 
55/8 


3^8 
4Vl6 

5Me 
7Vie 

9^6 


2  Vie 


5% 


!27/32 
27/82 


Tfc 


!5Ae 

?'* 

2% 

3% 


V4 

%6 


V2 
I 

1V4 

!5/8 


0.195 
0.260 
0.387 
0.514 
0.639 
1.014 
1.266 
1.642 


127&2 

2 


6% 


.625 
.600 
.602 
.602 
.623 
.630 
.626 
.625 


The  dimensions  given  above  for  regular  (full  length)  Morse  taper  shanks  are 
those  which  have  been  accepted  as  standard  and  are  used  by  most  manufacturers. 
In  a  recent  catalogue  of  the  Morse  Twist  Drill  &  Machine  Co.,  however,  a  table  is 
given  in  which  the  length  of  the  tang  and,  consequently,  the  whole  length  of  the 
shank  is  slightly  increased.  The  increase  in  length,  however,  is  so  slight  that  it 
does  not  prevent  the  shank  from  fitting  into  the  ordinary  standard  taper  socket. 


THE        STARRETT       BOOK 


TURNING  TAPERS.  Ordinary  tapers  are  rated  at 
the  amount  which  the  diameter  changes  in  a  foot's  length; 
as,  for  example,  the  Brown  &  Sharpe  taper  of  %  inch 
per  foot.  To  turn  a  taper  it  is  necessary  to  use  a  lathe 
provided  with  a  taper  attachment  or  to  adjust  the  foot- 
stock  of  the  engine  lathe  sufficiently  off  center  to  give 


TAPER  TURNING  IN  LATHE 
89 


THE       STARRETT       BOOK 

the  required  rate  of  diameter  change.  As  all  taper  attach- 
ments are  graduated  to  read  direct,  they  are  easily  set 
for  the  required  taper.  Adjustment  of  the  foot-stock  of 
an  engine  lathe  is  not  so  simple  as  the  taper  attachment. 
In  setting  the  taper  attachment,  the  axial  distance  the 
center  points  are  apart  is  not  important,  while  this  dis- 
tance must  be  considered  in  setting  over  the  foot-stock 
of  the  lathe. 

AMOUNT  TO  OFFSET  CENTERS  FOR  GIVEN 
TAPER.  If  the  distance  the  center  points  enter  the 
work  or  the  mandrel  is  ignored,  the  mandrel  length  can 
be  considered  as  the  distance  apart  of  the  center  points. 
The  calculation  necessary  to  determine  the  distance  which 
the  centers  shall  be  offset,  is  that  of  multiplying  the 
length  of  the  work  or  mandrel  in  feet  by  one-half  of  the 
required  taper  in  inches.  To  turn  a  Brown  &  Sharpe 
taper  on  a  piece  of  work  nine  inches  long  the  problem 
would  work  out  as  follows: 

.500         9  3 

_  x  -  -  =  0.1875  =  - 
2  12  16 

and  the  foot-stock  would  be  set  over  3Ae  inch. 

In  the  above  illustrative  example  both  length  and 
amount  of  taper  are  given,  but  the  amount  of  taper  is  not 
always  known.  Suppose  a  piece  is  8  inches  long  and  a 
taper  is  to  be  turned  on  one  end,  the  tapered  portion  to 
be  4  inches  long.  The  difference  in  diameters  of  these 
4  inches  is  to  be  %  inch.  How  much  must  the  tail  stock 
be  offset?  If  the  taper  is  %  inch  in  4  inches  it  would  be 
1%  inches  in  a  foot  and  the  tail  stock  would  be  moved 
over  one-half  of  1%  inches  or  %  inch,  if  the  piece  were  a 
foot  long,  but  as  it  is  only  8  inches  or  %  of  a  foot  long, 
the  tail  stock  should  be  moved  over  %  multiplied  by  % 
or  V2  inch.  Had  the  piece  been  18  inches  long,  the  tail 
stock  should  be  moved  over  %  multiplied  by  %  or  1% 
inches. 

90 


THE       STARRETT       BOOK 

It  has  been  assumed  for  these  simple  calculations 
that  the  lathe  centers  merely  touch  the  ends  of  the  piece, 
thus  making  the  length  of  the  piece  the  same  as  the  dis- 
tance between  centers.  But  in  actual  work  the  distance 
the  centers  enter  the  piece  must  be  considered.  The 
calculation  should  be  as  accurate  as  possible  to  avoid 
continually  changing  the  tail  stock  to  get  a  reasonably 
good  taper  fit.  The  necessity  of  considering  the  distance 
the  center  enters  the  piece  depends  somewhat  upon  its 
length.  If  the  piece  is  very  long,  the  actual  taper  will 
differ  considerably  from  the  calculated  taper.  If  each 
center  enters  the  piece  one-fourth  inch  they  would  enter 
a  total  of  one-half  inch,  and  the  length  of  the  piece 
should  be  reduced  by  one-half  inch  in  the  calculation. 
While  turning  the  taper  the  calipers  should  be  used  fre- 
quently so  that  it  may  be  soon  determined  whether  or  not 
the  tail  stock  is  correctly  placed. 

For  coning  pulleys,  set  the  foot-stock  away  from  the 
operator  when  adjusting.  In  most  taper  work,  however, 
the  center  is  offset  towards  the  operator. 

SETTING  THE  TOOL.  The  tool-point  should  be  set 
at  the  exact  height  of  the  axis  of  the  lathe. 

TESTING  THE  TURNED  TAPER.  To  test  the  taper 
as  it  is  turned,  ground,  or  filed,  it  should  be  pressed 
lightly  into  a  standard  tapered  hole  and  worked  back  and 
forth  sufficiently  to  mark  the  places  where  bearing  occurs. 
If  the  work  has  been  lightly  covered  with  some  marking 
pigment,  the  bearing  points  will  be  more  distinct.  Care, 
however,  must  obtain  that  the  coating  is  not  sufficient  to 
smooch,  as  it  will  deceive  the  workman.  Adjust  taper- 
setting  until  a  correct  fit  is  obtained. 

ECCENTRIC  TURNING.  While  for  the  most  part  the 
lathe  is  used  for  work  exactly  concentric  with  the  axis, 
it  can  be  used  for  turning  work  not  concentric  with  the 
axis.  Work  of  this  sort  is  termed  "eccentric,"  and  an 
example  of  such  work  is  seen  in  the  eccentrics  which 

91 


THE       STARRETT       BOOK 


Amount  of  Taper  in  a  Given  Length,  When  the  Taper  per 
Foot  is  Known  — Table  9 


°v< 

Taper  per  Foot 

j! 

Me 

%2 

tt 

Vi 

% 

* 

0.600 

% 

M 

1 

1V4 

Hi 

.0002 

.0002 

.0003 

.0007 

.0010 

.0013 

.0016 

.0016 

.0020 

0.0026 

0.0033 

T/ 

0003 

0005 

0007 

0013 

0020 

.0026 

.0031 

0033 

0039 

00052 

00065 

% 

.0007 

.0010 

.0013 

.0026 

.0039 

.0052 

.0062 

.0065 

.0078 

0.0104 

0.0130 

vie 

.0010 

.0015 

.0020 

.0039 

.0059 

.0078 

.0094 

.0098 

.0117 

0.0156 

0.0195 

^4 

.0013 

.0020 

.0026 

.0052 

.0078 

.0104 

.0125 

.0130 

.0156 

0.0208 

0.0260 

%6 

.0016 

.0024. 

.0033 

.0065 

.0098 

.0130 

.0156 

.0163 

.0195 

0.0260 

0.0326 

% 

.0020 

.0029 

.0039 

.0078 

.0117 

.0156 

.0187 

.0195 

.0234 

0.0312 

0.0391 

%e 

.0023 

.0034 

.0046 

.0091 

.0137 

.0182 

.0219 

.0228 

.0273 

0.0365 

0.0456 

Vz 

00?fi 

0039 

.0052 

0104 

.0156 

.0208 

.0250 

.0260 

.0312 

0.0417 

00521 

%e 

.0029 

.0044 

.0059 

.0117 

.0176 

.0234 

.0281 

.0293 

.0352 

0.0469 

0.0586 

.0033 

.0049 

.0065 

.0130 

.0195  .0260 

.0312 

.0326 

.0391 

0.0521 

0.0651 

Hie 

.0036 

.0054 

.0072 

.0143 

.0215 

.0286 

.0344 

.0358 

.0430 

0.0573 

0.0716 

% 

.0039 

.0059 

.0078 

.0156 

.0234 

.0312 

.0375 

.0391 

.0469 

0.0625 

0.0781 

1%e 

.0042 

.0063 

.0085 

.0169 

.0254 

.0339 

.0406 

.0423 

.0508 

0.0677 

0.0846 

% 

.0046 

.0068 

.0091 

.0182 

.0273 

.0365 

.0437 

.0456 

.0547 

0.0729 

0.0911 

1y^e 

.0049 

.0073 

.0098 

.0195 

.0293 

.0391 

.0469 

.0488 

.0586 

0.0781 

0.0977 

1 

.0052 

.0078 

.0104 

.0208 

.0312 

.0417 

.0500 

.0521 

.0625 

0.0833 

0.1042 

2 

.0104 

.0156 

.0208 

.0417 

.0625 

.0833 

.1000 

.1042 

.1250 

0.1667 

0.2083 

3 

.0156 

.0234 

.0312 

.0625 

.0937 

.1250 

.1500 

.1562 

.1875 

0.2500 

0.3125 

4 

.0208 

.0312 

.0417 

.0833 

.1250 

.1667 

.2000 

.2083 

.2500 

0.3333 

0.4167 

5 

.0260 

.0391 

.0521 

.1042 

.1562 

.2083 

.2500 

.2604 

.3125 

0.4167 

0.5208 

6 

.0312 

.0469 

.0625 

.1250 

.1875 

.2500 

.3000 

.3125 

.3750 

0.5000 

0.6250 

7 

.0365 

.0547 

.0729 

.1458 

.2187 

.2917 

.3500 

.3646 

.4375 

0.5833 

0.7292 

8 

.0417 

.0625 

.0833 

.1667 

.2500 

.3333 

.4000 

.4167 

.5000 

0.6667 

0.8333 

9 

.0469 

.0703 

.0937 

.1875 

.2812 

.3750 

.4500 

.4687 

.5625 

0.7500 

0.9375 

10 

.0521 

.0781 

.1042 

.2083 

.3125 

.4167 

.5000 

.5208 

.6250 

0.8333 

1.0417 

11 

0573 

.0859 

.1146 

.2292 

.3437 

.4583 

.5500 

.5729 

.6875 

0.9167 

1.1458 

12 

.0625 

.0937 

.1250 

.2500 

.3750 

.5000 

.6000 

.6250 

.7500 

1.0000 

1.2500 

92 


THE       STARRETT       BOOK 

operate  the  valves  of  steam  engines.  If  the  work  has  a 
hole  through  it,  as  in  the  above  example,  the  hole  is  first 
finished  to  required  dimensions.  A  mandrel  is  then  used 
for  carrying  the  work  on  the  centers.  While  the  mandrel 
has  been  built  on  one  set  of  centers  exactly  true  with  its 
axis,  for  eccentric  turning  it  has  a  second  set  of  centers 
which  are  offset  the  amount  required  for  the  eccentricity 
specified.  In  the  case  of  eccentrics  made  solid  with  the 


FIG.  28 

shaft,  the  two  sets  of  centers,  onet  for  turning  the  shaft 
and  the  other  for  finishing  the  eccentrics,  are  made 
side  by  side  in  the  ends  of  the  shaft,  as  shown  in  Fig.  28. 

When  the  specified  eccentricity  is  too  extreme  to 
allow  both  pairs  of  centers  coming  within  the  limits  of 
the  diameter  of  the  shaft,  special  ends  may  be  cast  or 
forged  on  the  ends  of  the  work,  and  can  afterward  be 
machined  off.  In  crank-shaft  turning,  special  attach- 
ments are  provided  for  the  ends  of  the  shaft.  Special 
eccentric  turning  chucks  .may  be  made  to  hold  the  work. 

CHUCKING.  Chucking  includes,  not  only  the  mount- 
ing of  the  work  in  the  chuck,  but  performing  the  neces- 
sary operations  on  it  while  so  held.  The  name  "chuck" 
is  given  to  a  line  of  tools  having  a  variety  of  form,  all 

93 


THE       S    T    A    R    R    E 


T       BOOK 


94 


THE       STARR   E    T    T       BOOK 

of  which  are  designed  to  hold  work  or  tools  upon  the 
nose  of  a  spindle.  In  general  the  heavier  sorts  are 
mounted  upon  a  face-plate  which  screws  upon  the  end 
of  the  spindle,  while  smaller  sizes  are  fitted  with  a  taper- 
shank  which  fits  tightly  into  the  tapered  hole  in  the 
spindle.  The  smaller  sizes  are  used  for  carrying  tools, 
such  as  drills,  also  screws,  studs,  wire  pins,  etc.;  and  are 
known  as  drill-chucks. 

The  larger  sizes  are  widely  used  for  holding  work 
for  machine  operations,  and  are  sometimes  called  "work- 
chucks."  On  their  face  they  are  provided  with  adjust- 
ing jaws  movable  regularly  to  and  from  the  center;  these 
jaws  are  so  designed  that  a  considerable  variety  of  work 
may  be  readily  held  and  successfully  worked  upon  with 
common  cutting  tools.  The  jaws  are  moved  by  means 
of  screws  or  gears,  and  can  be  adjusted  independently, 
the  chuck  being  called  an  independent  jaw-chuck;  or, 
all  the  jaws  may  be  made  to  move  together,  in  which 
case  it  is  known  as  a  Universal  chuck. 

HOLDING  THE  WORK.  The  work  must  be  clamped 
firmly  in  the  chuck  while  being  machined.  Care  must 
also  be  taken  that  the  clamping  of  a  slender  piece  is 
not  so  firm  as  to  distort  or  spring  it.  If  work  slips, 
tools  may  be  broken,  and  if  held  too  tightly  and  sprung 
or  crushed,  the  work  is  injured  and  in  some  cases  en- 
tirely ruined. 

TRUING  THE  WORK.  Adjusting  the  chuck-jaws 
so  that  the  work  will  run  as  true  as  desired  is  termed, 
"truing  up  the  work."  This  is  preliminary  to  any  tool- 
ing which  may  be  done  on  the  job.  Often  this  truing 
of  the  work  can  be  accomplished  by  holding  a  piece 
of  chalk  to  just  touch  the  work,  leaving  a  plain  mark- 
ing—  this  method  is  used  when  chucking  rough  pulleys 
for  drilling  out  the  hole  in  the  hub.  Where  greater 
accuracy  is  required,  the  work  is  indicated  with  a  Uni- 
versal dial  test  indicator. 

95 


THE       STARRETT       BOOK 

CHUCKING  TOOLS.  With  the  work  located  in  the 
chuck  it  may  be  tooled  with  ordinary  lathe  tools,  such 
as  shown  in  the  tool-chart  (page  70),  or  it  may  be  drilled 
with  two,  three,  or  four  fluted  twist  drills,  and  reamed 
with  machine  reamers,  or  special  shell  bits  and  coun- 
terbores. 

CHUCKS  ON  TURRET  LATHES.  In  turret  lathe- 
work,  for  bar-stock,  the  chuck  is  a  part  of  the  regular 
tool  equipment;  these  chucks  are  often  of  special  design, 
so  made  that  they  open  and  close  by  hand-operated 
levers  or  automatically-operated  cams. 

KNURLING.  The  surfaces  of  adjusting  screws  and 
small  machine  parts  are  often  given  a  regular  rough  sur- 
face for  easy  gripping.  In  the  machine  shop  this  is 
done  by  using  a  tool  known  as  a  "knurl"  or  "knurling 
tool,"  which  consists  of  one  or  more  indented  rollers  or 
knurls  mounted  to  rotate  in  some  form  of  holder. 


32nds. 
I     0312 

3     0937 
5    .1562 
7    .3187 
9    .2812 
II   .3437 


I- 

1-4-  .250 

3-8  .375 

IBths. 

.0625 
3    .1875 

5  .3125   NO  232 
7  .4375  15.4687 

THELaSTARRETTCD 
ATHOLMASS.USA 


FIG.  29 


These  knurls  are  forced 
into  and  fed  along  the  stock 
until  the  indented  design  has 
been  sufficiently  imprinted 
into  the  surface.  When  neatly 
and  effectively  done  the  re- 
sults give  a  fine  gripping  sur- 
face and  a  rather  pleasing  effect  to  the  eye.  The  knurling 
tool  may  be  fed  along  the  surface  of  the  work  by  hand, 
but  usually  the  power  traverse  feed  is  used.  The  process 
is  repeated  if  one  passage  of  the  tool  does  not  give  suffi- 
cient depth. 

Fig.  29  shows  knurling  on  a  micrometer. 


96 


THE       STARRETT       BOOK 


TOOL-MAKING 

Under  the  name  "tools"  are  listed  the  various  small 
or  tool-room  tools  used  either  by  hand  or  in  various  ma- 
chines. So  important  has  their  use  become  that  large 
industries  are  devoted  to  their  manufacture,  and  most 
machine-building  firms  now  buy  their  more  common 
tools  rather  than  maintain  a  tool-making  plant  of  their 
own.  For  example,  drills,  reamers,  milling  cutters, 
counterbores,  colletts,  etc.,  are  usually  purchased  in  the 
open  market.  Every  skilled  machinist,  however,  should 
know  the  principles  upon  which  such  tools  are  made, 
and  should  be  able  to  make  any  or  all  of  them. 

DRILLS.  Drills  are  now  largely  of  the  twist  type, 
and  the  most  efficient  are  machined  and  milled  from 
solid  bar-stock,  and  for  this  purpose  both  Carbon-tool 
steel  and  high-speed  steel  are  being  used.  The  prevailing 
type  has  a  straight  or  a  tapered  holding  shank,  spiral- 
milled  flutes  and  a  cone-point  with  effective  cutting  lips 
as  noted  under  drill  sharpening.  The  flutes  or  lands 
taper  slightly  from  full  diameter  size  at  the  cone-point 
to  several  thousandths  inch  smaller  at  or  near  the  hold- 
ing shank.  To  prevent  rubbing  on  the  sides  of  a  hole, 
the  flutes  are  also  cleared  back  from  the  front  edge 
throughout  their  length.  The  grooves  are  milled  with 
cutters  having  a  form  that  gives  the  maximum  chip 
capacity,  yet  leaves  the  cutting  edge  of  the  drill-lip  a 
straight  line. 

Several  makers  of  twist-drills  increase  the  lead  of 
the  twist  when  milling  the  grooves;  such  drills  are  known 
as  "increase  twist"  drills.  The  web  is  as  thin  as  con- 
sistent with  the  required  strength,  and  with  some  makers 
is  thicker  near  the  shank  than  at  the  point.  Drills 
are  carefully  heat-treated,  straightened,  and  ground  to 
diameter. 

REAMERS.    The  term  "reaming"  is  given  to  the  proc- 

97 


THE       STARRETT       BOOK 

ess  of  enlarging  a  drilled  hole.  Reamers  are  of  two  well- 
defined  types,  known  as  "fluted"  reamers  and  "rose" 
reamers.  The  fluted  reamer  is  one  having  numerous 
flutes  on  the  circumference  of  the  cutting  portion  of 
the  tool.  In  other  words,  the  cutting  is  done  on  the  cir- 
cumference instead  of  at  the  end,  as  with  a  drill. 

The  number  of  flutes  on  the  surface  of  a  reamer 
varies  with  the  diameter,  and  with  some  makes  the  num- 
ber of  flutes  is  greater  for  a  given  diameter  when  the 
reamer  is  to  be  used  in  a  machine  instead  of  for  hand 
reaming. 

As  its  name  implies,  a  fluted  hand  reamer  is  made 
for  hand  use,  and  is  seldom  called  upon  to  enlarge  a 
hole  more  than  .007"  for  any  diameter,  and  not  more 
than  .003"  in  the  smaller  sizes. 

In  the  case  of  machine  or  lathe  reamers,  the  length 
of  the  flutes  for  any  given  diameter  is  fifty  per  cent 
less  than  the  standard  length  for  hand  reamers.  The 
depth  of  flute  is  usually  somewhat  in  excess  of  that  of 
hand  reamers.  In  most  cases  machine  reamers  are  used 
for  enlarging  drilled  holes  to  a  diameter  which  only 
allows  sufficient  stock  for  hand  reaming.  When  the  holes 
are  not  to  exceed  a  diameter  in  length,  machine  reamers 
may  be  used  for  finishing  the  drilled  hole  to  its  full 
diameter;  but  when  straight,  round,  accurate  holes  are 
to  be  of  exact  diameter  the  better  practice  is  to  first  drill 
1/32"  to  1/16"  under  size,  enlarge  to  hand  reaming  size 
with  a  machine  reamer,  and  then  carefully  hand  ream  to 
exact  size. 

ECCENTRIC  FLUTES.  Formerly  fluted  reamers  had 
an  odd  number  of  flutes,  such  as  nine  or  eleven.  Although 
this  method  eliminated  chattering  to  some  extent,  it  had 
the  disadvantage  of  making  it  difficult  to  caliper  the 
diameter  of  the  cutting  edges.  Eccentric  fluting,  as  it 
is  called,  consists  in  milling  the  flutes  with  uneven  spac- 
ing to  obviate  chattering,  but  having  them  exactly  oppo- 

98 


THE       STARRETT       BOOK 

site,  so  that  a  diameter  measurement  may  be  made  with 
a  micrometer. 

A  rose-reamer  is  an  end-cutting  tool,  and  is  often 
used  in  place  of  a  drill  in  cored  holes.  It  is  never  made 
for  hand  use,  and  in  general  practice  is  seldom  used  for 
exact  diameter. 

MILLING  CUTTERS.  In  lathe  work  the  cutting  tool 
is  fixed  and  the  work  rotates.  In  a  milling  machine  the 
cutter  rotates  and  work  is  fed  against  it.  The  rotating 
cutter,  termed  a  "milling  cutter,"  has  an  almost  unlimited 
variety  of  sizes  and  shapes  for  milling  regular  and  irreg- 
ular forms.  Milling  cutters  are  made  from  some  of  the 
tool  steels,  heat-treated  to  give  the  right  cutting  quali- 
ties, the  stock  coming  to  the  tool-maker  in  the  form  of 
rough  blanks,  carefully  annealed.  Where  the  cutter  has 
a  hole  through  it  this  is  first  drilled,  bored,  or  reamed  to 
a  diameter  somewhat  smaller  than  that  in  the  finished 
cutter.  The  reason  for  this  is  that  all  the  exact  true  sur- 
faces must  be  finished  after  the  cutter  has  been  hardened 
—  some  grinding  process  being  necessary  which  requires 
an  excess  of  stock. 

When  the  length  of  the  cutter  is  greater  than  about 
one-half  inch,  it  is  usual  to  chamber  the  hole  to  a  shape 
that  renders  it  necessary  to  diameter  grind  the  holes  at 
the  ends  only.  In  cutters  of  considerable  length  the 
saving  in  grinding  by  this  procedure  is  considerable. 
The  sides  of  the  blanks  are  usually  recessed,  giving  a  hub- 
and-rim  effect  at  the  sides  of  the  cutter.  An  even  num- 
ber of  teeth  is  preferable,  and  these  are  spaced  to  a  cir- 
cumferential pitch  varying  from  three-eighths  to  three- 
quarters  inch  for  ordinary  cutter  sizes. 

When  the  teeth  are  milled  into  the  solid  blank,  a 
cutter  giving  a  space  angle  of  sixty  degrees  is  preferred 
for  cutting  the  peripheral  teeth,  while  one  of  seventy 
degrees  is  generally  used  for  the  side  teeth.  Where 
milling  cutters  are  made  in  quantity,  special  space  cutters 

99 


THE        STARRETT       BOOK 

are  worked  out  to  give  the  maximum  chip  room  con- 
sistent with  tooth  strength. 

After  the  cutter  has  been  heat-treated  to  the  proper 
hardness,  it  is  finished  to  the  specific  dimensions  by 
grinding. 

GRINDING  THE  HOLE.  Unless  special  methods 
and  tools  are  employed  the  hole  is  completely  finished 
as  the  first  operation  of  grinding.  This  is  accomplished 
by  holding  the  cutter  trued  in  a  chuck  screwed  on  the 
spindle  of  a  Universal  grinder  and  grinding  out  the  hole 
to  standard  size,  using  an  internal  grinding  attachment. 

GRINDING  THE  SIDES.  Fig.  30  shows  how  to 
grind  the  sides  with  the  cutter  held  flat  against  a  face- 
plate. If  the  cutter  is  to  be  used  for  deep  cuts,  the  face- 
plate is  set  to  give  a  slight  concavity  to  the  sides  of 
the  cutter. 


FIG.  30 


CLEARANCE  OF  THE  TEETH.  The  teeth  of  milling 
cutters  are  given  a  slight  clearance  back  from  the  cutting 
edges;  five  degrees  is  usually  sufficient. 

100 


THE       STARRETT       BOOK 


JIGS  AND   FIXTURES 

Jigs  and  fixtures  are  special  devices  designed  to  put 
manufacturing  upon  an  efficient  basis.  Three  distinct 
purposes  are  served  by  the  use  of  jigs:  (a)  Reduction  of 
cost  per  piece;  (&)  interchangeability  of  parts;  and  (c) 
accurate  production. 

Jigs  and  fixtures  are  usually  made  from  cast  iron  or 
steel.  Their  use  practically  does  away  with  fitting,  as 
this  term  is  known  in  shops  not  using  jigs. 

JIG  DESIGN.  A  jig  is  a  device  for  holding  the 
work  and  for  locating  the  tool  work  to  be  done  upon  it. 
A  good  example  of  this  is  shown  in  the  drill  jig,  Fig.  31. 

Jigs  are  of  the  plate  type  which  lies  upon  and  is 
clamped  to  the  surface  of  the  work;  of  the  open-box 
type;  and  of  the  closed-box  type. 

In  designing  a  jig,  the  piece  is  first  drawn  upon  a 
sheet  of  paper,  which  is  sufficiently  large  to  allow  locat- 
ing the  views  some  distance  apart.  This  permits  build- 
ing the  jig  in  the  drawing  around  the  "coupon,"  as  the 
piece  is  often  called.  To  start  the  design,  first  determine 
and  lay  down  the  locating  points  or  stops,  then  arrange 
the  clamping  device.  A  jig  should  be  so  designed  that 
the  work  can  be  put  into  position  in  only  one  way. 
Provide  for  supporting  the  thrust  of  the  cutting  tools 
in  such  a  manner  as  to  avoid  springing  the  work.  Make 
the  jig  as  simple  as  possible,  avoiding  every  feature  in 
design  that  complicates  the  workman's  use. 

While  in  the  larger  shops  the  jigs  are  designed  by 
the  draftsmen,  in  many  shops  the  tool-maker  both  de- 
signs and  builds  the  jigs,  and  in  no  other  way  can  a 
workman  so  clearly  show  his  ability  and  ingenuity  as 
in  the  building  of  jigs. 

JIG  BODY.  The  jig  body  is  usually  of  cast  iron, 
which  is  first  rough  planed  or  milled  on  all  surfaces 
which  are  to  be  finished.  These  surfaces  are  then  finish 

101 


THE        STARRETT       BOOK 

planed  to   final   dimensions.     In   some   cases  jig  bodies 
are  finished  by  grinding  in  a  surface  grinder. 

LOCATING  BUSHING  HOLES.  If  no  particular 
accuracy  is  demanded,  the  holes  for  bushings  can  be 
located  directly  by  careful  attention  to  ordinary  laying- 
out  methods,  and  the  hole  drilled  and  reamed  directly. 


FIG.  31 

When  the  allowable  error  is  very  small  a  more  accurate 
scheme  must  be  followed,  and  the  best  of  several  meth- 
ods for  the  average  tool-maker  is  that  known  as  the 
button  method.  In  this  the  holes  are  located  by  laying 
out  scribed  center  lines  and  locating  intersections  where 
the  holes  are  to  be  centered.  Instead  of  drilling  and 
reaming  the  bushing  holes,  holes  are  drilled  and  tapped 
to  fit  the  button  screws.  The  jig  buttons  are  small, 
accurately  ground  cylinders,  as  shown  in  Fig.  32.  These 
are  held  by  means  of  the  screws,  lightly  clamped  in  place, 


102 


THE        STARRETT       ROOK 


and  exactly  located  to  centers  by  accurate  measurements. 
The  highest  possible  accuracy  in  locating  holes  is  secured 
bv  this  method. 


FIG.  32 

BORING  HOLES.  The  holes  for  the  hardened  bush- 
ings are  usually  bored  by  swinging  the  jig  body  upon  a 
face-plate  in  an  engine  lathe.  The  jig  body  is  then 
shifted  upon  the  face-plate  until  a  button  indicates  true 


THE        STARRETT       BOOK 

with  a  Universal  Dial  Indicator,  as  shown  in  Fig.  33. 
The  jig  body  is  then  clamped  tightly  upon  the  face-plate. 
After  removing  the  jig  button,  the  hole  is  first  rough- 


ADJUSTING  BUTTONS  TO  SIDE  OF  PLATE 


BUTTONS  IN  PLACE 


ADJUSTING  BUTTONS  WITH  MICROMETER 
104 


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106 


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drilled  approximately  to  size,  and  afterwards  carefully 
bored  exactly  to  size.  This  prepares  the  hole  for  hold- 
ing the  hardened  steel  bushing;  the  process  is  repeated 
for  all  the  previously  located  buttons. 

JIG  BUSHINGS.  If  the  holes  in  a  cast-iron  or  soft- 
steel  jig  body  were  left  as  bored,  they  would  soon  lose 
accuracy  by  wearing  off  center;  To  prevent  this  wear 
the  holes  are  lined  with  hardened  and  carefully  ground 
bushings,  pressed  or  driven  tightly  into  place.  These 


bushings  are  made  with  a  hole  having  a  diameter  equal 
to  that  of  the  tool  which  passes  through  them.  The 
bushings  are  sufficiently  long  to  support  the  drill.  In 
case  the  jig  bushings  must  be  removed  frequently,  they 
are  known  as  slip  bushings,  and  the  hole  in  which  they 
slip  is  lined  with  a  steel  lining,  itself  hardened  and 
ground.  In  some  cases  the  bushing  locates  the  work  as 
well  as  the  tool,  and  if  so  the  bushing  screws  through 
the  body  of  the  jig  and  against  some  prominent  part  of 
the  work,  as  a  boss  for  example. 


107 


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TOLERANCES.  In  all  construction  work  a  certain 
amount  of  inexactness  is  allowable.  In  other  words, 
it  is  impossible  to  obtain  absolute  precision,  and  the 
allowable  errors  in  exactness  are  termed  "tolerances." 
In  some  cases  a  tolerance  of  one-sixteenth  inch  might 
be  allowed,  while  in  others  exactness  to  the  fraction  of 
a  thousandth  part  of  an  inch  may  be  necessary.  See 
pages  31  and  32. 


JIG  FOR  DRILLING  BOLT  HOLES  IN  CYLINDER  FLANGE  AND  HEAD 

The  projection  on  the  jig  keeps  it  concentric  with 
the  bore  of  the  cylinder,  and  the  recess  fits  over  the  pro- 
jection on  the  head. 

108 


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GRINDING 

In  the  machine  shop  the  term  "grinding"  refers  to 
the  producing  of  finished  surfaces  by  means  of  rotating 
grinding  wheels,  and  the  process  of  grinding  as  used 
in  finishing  machine  parts  is  to-day  the  most  efficient 
method  devised  for  the  purpose.  With  a  proper  selec- 
tion of  grinding  machine  and  grinding  wheel,  all  of  the 
common  machine  construction  materials  may  be  readily 
and  accurately  finished. 

Grinding  machines  are  classified  into  two  groups, 
(a)  those  for  curved  surfaces;  as,  for  example,  cylin- 
drical work;  and  (5)  those  for  plane  or  flat  surfaces. 
The  first  of  these  is  usually  called  a  cylindrical  grinder, 
and  the  second  is  known  as  a  surface  grinder.  Each 
group  has  many  designs,  made  necessary  by  the  varied 
uses  to  which  grinding  is  adapting  itself. 

GRINDING  WHEELS.  These  are  now  known  as 
abrasive  wheels,  and  the  material  from  which  they  are 
made  is  termed  an  abrasive.  The  abrasives  in  common 
use  are  the  minerals  emery  and  corundum,  and  the 
manufactured  abrasives,  sold  under  the  trade  names  of 
Alundum,  Aloxite,  Carborundum,  Crystolon.  Owing  to 
the  uniformity  of  the  product  as  it  comes  from  the 
electric  furnace,  manufactured  abrasives  are  at  present 
more  largely  used  than  natural  abrasives. 

MAKING  ABRASIVE  WHEELS.  An  abrasive  wheel 
is  made  up  of  one  of  the  above-named  ABRASIVES  and 
a  BOND.  The  bond  is,  as  its  name  indicates,  something 
for  holding  the  abrasive  in  mixture.  Grinding  wheels 
are  made  by  three  processes,  known  as  Vitrified,  Silicate, 
and  Elastic. 

VITRIFIED  WHEELS.  In  wheels  made  by  the  Vitri- 
fied process,  the  bond  is  of  earth  or  clay  which  hardens 
or  vitrifies'  when  subjected  to  a  temperature  of  about 
2500°  F.  to  2800°  F.  for  a  definite  period  of  time.  Vari- 

109 


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Allowances  for  Grinding — Table  10 


Diameter, 
Inches 

Length,  Inches 

3 

6 

9 

12 

15 

18 

24 

30 

36 

42 

48 

Allowance,  Inches 

X 
K 

i 

1M 
U4 

2 
2K 

VA 

3 

3^ 
4 

V/2 

5 
6 

7 
8 
9 
10 
11 
12 

0.010 
0.010 
0.010 
0.010 
0.010 
0.015 
0.015 
0015 

0.010 
0.010 
0.010 
0.010 
0.015 
0.015 
0.015 
0.015 

0.010 
0.010 
0.010 
0.015 
0.015 
0.015 
0.015 
0.015 

0.010 
0.010 
0.015 
0.015 
0.015 
0.015 
0.015 
0.020 

0.015 
0.015 
0.015 
0.015 
0.015 
0.015 
0.020 
0.020 

0.015 
0.015 
0.015 
0.015 
0.015 
0.020 
0.020 
0.020 

0.015 
0.015 
0.015 
0.015 
0.020 
0.020 
0.020 
0020 

0.020 
0.020 
0.020 
0.020 
0.020 
0.020 
0.020 
0.020 

0.020 
0.020 
0.020 
0.020 
0.020 
0.020 
0.020 
0.025 

0.020 
0.020 
0.020 
0.020 
0.020 
0.020 
0.025 
0.025 

0.020 
0.020 
0.020 
0.020 
0.020 
0.025 
0.025 
0.025 

0015 

0015 

0.020 

0.020 

0020 

0.020 

0.020 

0.025 

0.025 

0.025 

0.025 

0.015 
0.020 
0.020 
0.020 
0.020 
0.020 
0.025 
0.025 
0.025 
0.025 
0.030 

0.020 
0.020 
0.020 
0.020 
0.020 
0.025 
0.025 
0.025 
0.025 
0.025 
0.030 

0.020 
0.020 
0.020 
0.020 
0.025 
0.025 
0.025 
0.025 
0.025 
0.030 
0.030 

0.020 
0.020 
0.020 
0.025 
0.025 
0.025 
0.025 
0.025 
0.030 
0.030 
0.030 

0.020 
0.020 
0.025 
0.025 
0.025 
0.025 
0.025 
0.030 
0.030 
0.030 
0.030 

0.020 
0.025 
0.025 
0.025 
0.025 
0.025 
0.030 
0.030 
0.030 
0.030 
0.030 

0.025 
0.025 
0.025 
0.025 
0.025 
0.030 
0.030 
0.030 
0.030 
0,030 
0.030 

0.025 
0.025 
0.025 
0.025 
0.030 
0.030 
0.030 
0.030 
0.030 
0.030 
0.030 

0.025 
0.025 
0.025 
0.030 
0.030 
0.030 
0.300 
0.300 
0.030 
0.030 
0.030 

0.025 
0.025 
0.030 
0.030 
0.030 
0.030 
0.030 
0.030 
0.030 
0.030 
0.030 

0.025 
0.030 
0.030 
0.030 
0.030 
0.030 
0.030 
0.030 
0.030 
0.030 
0.030 

110 


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ous  grades  of  hardness  are  obtained  by  using  bonds  of 
different  tensile  strength.  The  ideal  bond  is  one  which 
retains  the  grains  of  abrasive  until  sufficiently  dulled 
by  use,  and  then  allows  them  to  break  away,  and  in  this 
manner  bring  fresh  cutting  edges  and  points  into  grind- 
ing contact. 

SILICATE  WHEELS.  Silicate  of  Soda  is  the  bond 
used  in  silicate  wheels;  and  wheels  made  by  this  proc- 
ess are  most  efficient  for  tool  and  knife  grinding. 

ELASTIC  WHEELS.  This  process  of  bonding  is 
generally  used  for  the  very  thin  wheels  used  for  slitting 
metals.  The  principal  ingredient  of  the  bond  is  shellac. 

GRADING  THE  ABRASIVE.  By  numerous  crushing, 
grinding,  cleansing,  and  sorting  processes,  the  abrasive  is 
graded  into  a  series  of  sizes  which  give  the  wheel  its 
grain  number.  This  number  conforms  to  the  sieve  mesh 
through  which  the  abrasive  is  passed;  for  example,  grain 
No.  40  indicates  that  the  abrasive  was  graded  through  a 
sieve  having  a  mesh  of  forty  to  the  linear  inch. 

COMBINATION  WHEELS.  For  many  grinding  pur- 
poses the  combination  wheel  is  preferred  to  a  wheel  of 
single  grade.  Combination  wheels  are  made  up  of  abra- 
sives of  several  grain  numbers. 

BONDING.  The  ideal  bond  is  one  which  is  imper- 
vious to  moisture,  does  not  soften  by  heat,  and  which 
holds  firmly  the  cutting  points  of  the  abrasive  until  they 
become  dulled  by  use.  The  bond  then  releases  the  dull 
abrasive  and  permits  fresh,  sharp  points  to  begin  cutting. 
With  abrasives  of  equal  quality  the  maker  who  nearest 
approaches  the  ideal  bond  produces  the  superior  wheel. 

GRADING  THE  WHEELS.  In  grinders'  language, 
abrasive  wheels  are  known  as  hard  wheels  and  soft 
wheels.  The  maker,  therefore,  lists  his  wheels  as  hard 
or  soft  by  some  scale  of  numbers  or  by  letters.  A  prom- 
inent firm  uses  the  letters  of  the  alphabet,  as  shown  in 
the  following  list  in  which  "M"  is  medium. 

Ill 


THE       STARRETT       BOOK 

Norton  Grade  List 

The  following  grade  list  is  used  to  designate  the 
degree  of  hardness  of  our  Vitrified  and  Silicate  Wheels, 
both  Alundum  and  Crystolon. 

E Soft 

F 
G 
H 

I Medium  Soft 

J 
K 
L 

MEDIUM M MEDIUM 

N 
O 
P 

Medium  Hard Q 

R 
S 
T 

Hard U 

V 
W 
X 
Extremely  Hard Y 


The  intermediate  letters  between  those  designated  as 
soft,  medium  soft,  etc.,  indicate  so  many  degrees  harder 
or  softer;  e.  g.,  L  is  one  grade  or  degree  softer  than  me- 
dium; O,  two  degrees  harder  than  medium,  but  not  quite 
medium  hard. 

Elastic  Wheels  are  graded  as  follows:  1,  1 V2,  2,  2^,  3, 
4,  5,  and  6.  Grade  1  is  the  softest  and  grade  6  the  hardest. 

112 


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CYLINDRICAL  GRINDING.  When  the  piece  being 
ground  is  rotated,  the  process  is  known  as  cylindrical 
grinding,  and  the  development  of  machines  for  grind- 
ing cylinders  has  given  the  process  a  great  impetus. 
While  it  is  possible  to  grind  from  the  rough  stock  with- 
out previous  lathe  work,  the  method  usually  followed  is 
to  first  rough  turn  the  work. 

ROUGHING  FOR  GRINDING.  This  process  includes 
the  work  done  in  removing  excess  stock  previous  to 
finishing  to  size  in  the  grinding  machine.  Unless  a  study  is 
made  of  the  conditions  surrounding  the  whole  operations 
of  the  lathe  and  the  grinding  machine,  lack  of  efficiency 
may  result.  In  general  where  the  work  is  to  be  ground  it 
is  best  to  consider  the  lathe  as  a  mere  roughing  machine 
for  removing  the  excess  of  stock  at  as  deep  a  cut  and  as 
coarse  a  feed  as  is  consistent  with  an  efficient  cutting 
speed,  leaving  the  job  of  finishing  to  the  grinding  machine. 

AMOUNT  TO  LEAVE  FOR  GRINDING.  If  the  grind- 
ing machine  is  modern  in  design  as  much  as  1/32  of  an 
inch,  or  even  more  may  be  left  on  machinery  steel  parts 
for  removal  in  the  grinder;  the  amount  varying  with 
the  size  of  the  work  itself.  An  allowance  of  1/64  of  an 
inch  is  general  on  the  smaller  machine  parts,  but  this 
allowance  should  be  increased  on  larger  sizes.  Table  10, 
page  110,  shows  allowance  for  grinding  as  recommended 
by  one  maker  of  grinding  machines,  and  Table  11  shows 
grinding  wheel  speeds. 

SELECTING  THE  WHEEL,  the  selection  of  the 
wheel  to  be  used  in  any  grinding  operation  can,  per- 
haps, best  be  made  by  reference  to  Table  12,  page  115, 
which  fairly  represents  general  practice.  As  the  hard- 
ness of  material  and  the  area  of  contact  made  by  the 
wheel  have  a  marked  influence,  no  table  can  entirely 
solve  the  problem,  but  it  may  be  used  as  a  start  in  the 
right  direction.  In  general  a  soft  wheel  should  be  used 
on  hardened  work  and  a  harder  wheel  on  soft  materials. 

113 


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Table  of  Grinding  Wheel  Speeds— Table  11 


Diameter  Wheel 

Millimeters 

Rev.  per  Minute  for 
Surface  Speed  of 
4.000  Feet, 
or  1,200  Meters 

Rev.  per  Minute  for 
Surface  Speed  of 
5,000  Feet, 
or  1,500  Meters' 

Rev.  per  Minute  for 
Surface  Speed  of 
5,000  Feet, 
or  i,  800  Meters 

1  inch 

about      25 

15,279 

19,099 

22,918 

2    " 

50 

7,639 

9,549 

11,459 

3    " 

75 

5,093 

6,366 

7,639 

4     ' 

100 

3,820 

4,775 

5,730 

5     ' 

125 

3,056 

3,820 

4,584 

6     ' 

150 

2,546 

3,183 

3,820 

7     ' 

175 

2,183 

2,728 

3,274 

8     ' 

200 

1,910 

2,387 

2,865 

10     ' 

250 

1,528 

1,910 

2,292 

12     f 

305 

1,273 

1,592 

1,910 

14     ' 

355 

1,091 

1,364 

1,637 

16     ' 

405 

955 

1,194 

1,432 

18     ' 

455 

849 

1,061 

1,273 

20     ' 

505 

764 

955 

1,146 

22     ' 

515 

694 

868 

1,042 

24     ' 

610 

637 

796 

955 

26     ' 

660 

586 

733 

879 

28     ' 

710 

546 

683 

819 

30     ' 

760 

509 

637 

764 

32     ' 

810 

477 

596 

716 

34     ' 

860 

449 

561 

674 

36     ' 

910 

424 

531 

637 

38     ' 

965 

402 

503 

603 

40     ' 

'      1,015 

382 

478 

573 

42     ' 

1,065 

364 

455 

546 

44     « 

'     1,115 

347 

434 

521 

46     ' 

'  '     1,165 

332 

415 

498 

48     ' 

'     1,220 

318 

397 

477 

50     ' 

'     1,270 

306 

383 

459 

52     ' 

'     1,320 

294 

369 

441 

54     ' 

'     1,370 

283 

354 

425 

56     ' 

'     1,420 

273 

341 

410 

58     ' 

"     1,470 

264 

330 

396 

60    " 

"      1,520 

255 

319 

383 

The  R.  P.  M.  at  which  wheels  are  run  is  dependent  on  conditions  and  style 
of  machine  and  the  work  to  be  ground. 

Wheels  are  run  in  actual  practice  from  4,000  to  6,000  feet  per  minute;  in  some 
instances  as  high  as  7,500  feet. 


114 


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Grade  and  Grain  of  Grinding  Wheels  for  Different  Materials* 

Table  12 

(The  Norton  Co.) 


Class  of  Work 

Alundum 

Crystolon 

Grain 

Grade 

Grain 

Grade 

Aluminum  castings  

36  to  46 

3  to  4 
Bias. 

20  to  24 

20  to  24 
24  to  36 
16  to  24 
16  to  24 
30  to  46 
16  to  30 
20  to  30 
16  to  24 
20  to  30 
20  to  30 

PtoR 

QtoR 
PtoR 
PtoR 
OtoQ 
JtoL 
JtoL 
QtoS 
QtoS 
Q 
OtoQ 

Brass  or  bronze  castings  (large)  — 
Brass  or  bronze  castings  ^small)  — 
Car  wheels  cast  iron 

Car  wheels,  chilled  
Cast  iron,  cylindrical  
Cast  iron,  surfacing  
Cast-iron  (small)  castings  
Cast-iron  (large)  castings  
Chilled  iron  castings  
Dies  chilled  iron   . 

20 
24  comb. 
20  to  46 
24  to  30 
16  to  20 
20  to  30 

JtoK 
HtoK 
PtoR 
QtoR 
PtoU 

Dies,  steel  

36  to  60 
20  to  30 

JtoL 
PtoR 

Drop-forgings  
Internal  cylinder  grinding  .  .  .,  
Internal  grinding,  hardened  steel 
Machine  shop  use,  general  
Malleable  iron  castings  (large)  
Malleable  iron  castings  (small)  
Milling  cutters,  machine  grinding  .  . 
Milling  cutters,  hand  grinding  
Nickel  castings  
Pulleys,  surfacing  cast  iron  
Reamers,  taps,  etc.,  hand  grinding.  . 
Reamers,  taps,  special  machines  — 
Rolls  (cast  iron)  wet 

30  to  60 

ItoL 

46  to  60 
20  to  36 
14  to  20 
20  to  30 
46  to  60 
46  to  60 
20  to  24 

46  to  60 
46  to  60 
24  to  36 
70 

JtoM 
OtoQ 
PtoU 
PtoR 
HtoM 
JtoM 
PtoQ 

KtoO 
JtoM 
JtoM 
!Hto2 
Elas. 

"RtoS 
QtoS 

R  ' 
KtoL 

16  to  20 
20  to  30 

20  to  25 

30  to  36 

24  to  38 

70  to  80 

30  to  46 
30  to  50 

jtoM' 

I^to2 
Elas. 
2  to  3  Elas. 
KtoM 

Rolls  (chilled  iron),  finishing  

Rubber  .'  

30  to  50 
36  to  50 
60 
24  comb. 
46  to  60 
24  to  36 
24  comb. 
46  to  60 
36  to  46 
12  to  20 
20  to  30 
16  to  46 
16  to  24 
46  to  60 
36  to  60 
12  to  30 
46  to  60 

JtoK 
MtoN 
OtoQ 
LtoN 
LtoN 
HtoK 
K 
JtoL 
HtoK 

SSS 

LtoP 
PtoR 
M 
KtoM 
PtoU 
KtoM 

Saws,  gumming  and  sharpening  .... 
Saws,  cold  cutting-off  

Steel  (soft),  cylindrical  grinding.  .  .  j 

Steel  (soft),  surface  grinding  
Steel  (hardened),  cylindrical  grind-  5 
ing  { 
Steel  (hardened),  surface  grinding  .  . 
Steel,  large  castings  

:  ::::; 

Steel  (manganese),  safe  work  
Structural  steel                

Twist  drills,  special  machines  

Wonrlwnrkincr  tnnls  .  . 

*  The  information  contained  in  this  table  is  general  and  intended  only  to  give 
an  approximate  idea  of  the  grade  used  under  ordinary  conditions. 

116 


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MOUNTING  THE  WHEEL.  The  wheel  should  be 
so  mounted  that  there  are  no  unequal  stresses  set  up. 
Suitable  guards  should  be  provided  to  prevent  injury 
to  the  workmen  in  case  of  the  wheel  bursting.  The 
accompanying  illustrations  show  RIGHT  and  WRONG 
methods  of  mounting  wheels  —  carefully  study  the  cuts. 


MEASURING  THE  WORK.  The  use  of  micrometers 
for  obtaining  exact  measurements  is  nowhere  better 
illustrated  than  in  grinding.  Fig.  34  shows  an  oper- 
ator adjusting  his  micrometer  for  obtaining  a  measure- 
ment on  a  cylindrical  piece,  and  Fig.  35  shows  the 
operator  as  he  makes  his  reading.  While  in  lathe 
work  the  position  of  the  operator  leads  naturally  to 
adjusting  the  micrometer  spindle  with  the  fingers  of 
the  right  hand,  the  left  hand  grasping  the  frame,  in 
grinder  work  the  reverse  is  generally  true,  hence  he 
occupies  the  position  as  shown. 

GRINDING  FLAT  SURFACES.  Flat  surface  grind- 
ing may  be  divided  into  two  general  classes :  (a)  Machine 

116 


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FIG.  34 

parts,  such  as  boxes,  tables,  cross-slides,  faces  of  nuts, 
etc.;  and  (b)  fine  tool  work,  as,  for  example,  steel  blades, 
scales  and  rulers,  straight  edges,  etc.  Until  recently  the 
first-named  class  of  work  was  done  by  reciprocating 
the  work  beneath  the  circumferential  face  of  an  abrasive 
wheel  in  a  machine  which,  in  principle,  is  not  unlike  a 
small  planer.  The  use  of  machines  with  CUP  WHEELS 
has  practically  revolutionized  such  grinding,  and  an 
exactness  of  surface  is  being  obtained  on  fine  flat  work 
which  leaves  little  to  be  desired. 

LAPPING.  In  certain  lines  of  work  the  final  grind- 
ing process  is  often  made,  not  with  abrasive  wheels  as 
previously  described,  but  by  using  metal  discs,  rings,  or 
cylinders,  the  surfaces  of  which  have  been  charged  with 
a  fine  flour  abrasive.  Such  a  tool  is  called  a  "lap,"  and 
its  use  "lapping."  Laps  were  first  used  by  lapidaries  in 
finishing  the  surfaces  of  mineral  specimens,  but  laps 
have  been  in  common  use  for  a  considerable  time  on  fine 
work  in  the  machine  shop. 

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THE        STARRETT        BOOK 


Laps  are  generally  made  of  some  material  soft 
enough  so  that  the  abrasive  can  be  readily  pressed  into 
the  surface;  or,  as  it  is  correctly  termed,  the  surface 
is  "charged."  Soft,  close-grained  cast  iron,  copper, 
brass,  or  lead  may  be  used  for  the  lap,  and  any  of  the 
flour  abrasives  may  be  charged  into  the  surface  by  roll- 
ing the  abrasive  into  the  lap  either  with  a  hardened  roll 
or  on  a  hardened  surface. 


FIG.  35 

In  some  of  the  finer  grinding  operations  the  lap  is 
charged  with  diamond  dust  which  has  been  precipitated 
or  settled  in  a  suitable  dish  of  olive  oil.  The  several 
grades  are  denoted  by  the  time  taken  to  precipitate;  as, 
for  example,  fineness  No.  5  takes  ten  hours. 

Since  lapping  is  a  somewhat  slow  and  tedious  proc- 
ess it  should  be  used  only  for  the  removal  of  small 
amounts  of  stock. 

COMMON  USES  OF  LAPPING.  The  more  common 
uses  of  lapping  are  those  of  finishing  micrometer  ends, 
plug  and  ring  gages,  holes  in  jig  bushings,  and  in  the 
finest  die  and  punch  work. 

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THE       STARRETT       BOOK 

LOCATING  AND  ALIGNING 
MACHINERY 

When  the  product  of  the  shop  is  determined,  the 
proper  location  of  the  machines  may  be  found  by  means 
of  a  plan  or  location  drawing  worked  out  in  the  draft- 
ing room.  An  easy  way  to  do  this  is  to  provide  rectangu- 
lar slips  of  cardboard,  each  representing  to  some  definite 
scale  the  plan  outline  of  each  machine.  Placing  these 
upon  the  floor  plan  of  the  room,  the  better  of  several 
arrangements  may  be  found,  and  by  using  push  pins  the 
cardboard  representations  may  be  fixed  in  position. 


FIG.  36 

Having  decided  upon  the  location,  the  machinery 
may  be  aligned  in  these  positions  by  measurements  from 
some  base  line  made  upon  the  floor  or  ceiling;  or  a 
leveling  instrument,*  such  as  shown  in  Fig.  36,  may 
be  used. 

Ordinarily  the  machines  are  aligned  by  simple  meas- 

*  See  page  124  for  directions  for  setting  up  a  level. 
119 


THE        STARRETT       BOOK 

urements  and  the  countershafting  hung  from  the  ceil- 
ing vertically  over  the  machine  by  plumbing  up  from 
the  previously  located  machines.  In  such  work  thought 
must  always  be  given  to  the  line  shafting  and  pulleys. 

Unless  care  is  used,  there  may  be  such  interferences 
as  to  necessitate  repeating  the  work.  As  the  efficiency 
of  the  shop  depends  to  a  considerable  extent  on  a  con- 
venient arrangement  of  the  machines,  all  interferences 
should  be  taken  care  of  on  the  ceiling  rather  than  alter- 
ing the  arrangement  of  the  machines. 

ALIGNING  THE  SHAFTING.  With  the  locations  of 
the  several  lines  of  shafting  determined  upon,  the  usual 
method  of  alignment  is  to  stretch  a  wire  or  cord  the 
length  of  the  room  at  the  desired  level  of  the  shaft  and 
at  a  distance  from  its  location  sufficiently  great  to  give 
easy  working  room.  With  the  two  ends  of  the  wire  in 
position  it  should  be  stressed  to  bring  it  taut  and  should 
be  supported  at  frequent  intervals  by  wire  hangers. 


FIG.  37 

With  the  shafting  hangers  in  approximate  position 
and  the  shafting  in  place,  the  necessary  shifts  can  be 
made  to  bring  the  shaft  parallel  with  the  wire.  A  light 
stick  notched  at  one  end  to  rest  upon  the  shaft  and  a 
wire  brad  at  the  other  end  for  a  feeler  is  all  that  is  neces- 
sary for  ordinary  alignment.  Leveling  the  shaft  is  done 
with  special  spirit  levels  having  metal  frames,  the  bases 
of  which  have  been  carefully  grooved  to  set  upon  the 
shaft.  Such  a  level  is  shown  in  Fig.  37.  Special  level- 
ing and  aligning  attachments  for  setting  and  lining  up 

120 


THE        STARRETT       BOOK 

shafting  are  sometimes  used.  Shafting  is  often  lined  by 
plumbing  up  from  a  data  line  on  the  shop  floor  with  a 
mercury  plumb  bob. 


Mercury  Plumb 
Bobs 


121 


THE       STARRETT       BOOK 


LEVELING  INSTRUMENT 

While  the  surveyors'  transit  can  be  used  in  shop  level- 
ing and  in  shaft  aligning  a  much  simpler  and  a  more 
inexpensive  instrument  termed  a  leveling  instrument  is 
all  that  is  needed. 

It  consists  of  a  table  capable  of  being  adjusted  in  the 
horizontal  plane,  which  carries  a  yoke  which  in  turn 
carries  a  twelve-inch  brass  tube.  The  whole  instrument 
is  placed  upon  a  suitable  tripod.  The  tube  has  no  lenses 
and  therefore  is  not  a  telescope  as  in  the  surveyors' 
instrument. 

At  one  end  of  the  tube  are  the  usual  cross  hairs 
which  locate  the  axis  and  at  the  opposite  end  is  a  peep 
hole  or  sight  piece  for  the  eye.  The  yoke  which  carries 
the  tube  is  attached  to  a  graduated  arc  which  is  let  into 
the  upper  part  of  the  table;  this  allows  the  instrument 
to  swing  to  read  angles  in  the  horizontal  plane. 

ADJUSTING  THE  INSTRUMENT.  In  using  this  in- 
strument it  is  important  that  the  table  be  carefully  lev- 
eled. It  is  pivoted  on  the  tripod  tube  by  a  ball  and  socket 
joint.  Three  knurled-head  adjusting  screws  threaded 
through  the  tripod  top  and  resting  against  the  under  side 
of  the  table  furnish  a  means  of  adjusting  the  table.  Upon 
the  table  carrying  the  yoke  is  a  bent-tube  spirit  level  with 
a  sensitive  air  bubble.  After  the  tripod  legs  have  been 
placed  to  roughly  level  the  instrument,  adjust  the  knurled 
leveling  screws  to  give  .as  correct  a  centering  for  the 
air  bubble  as  is  possible.  To  test  this  adjustment  swing 
the  yoke,  which  carries  the  air  bubble,  to  several  posi- 
tions and  note  any  change  in  the  position  of  the  bubble. 
If  there  is  a  change,  readjust  the  leveling  screws  until 
the  yoke  can  be  swung  through  its  travel  with  the  air 
bubble  maintaining  its  central  position. 

USING  THE  LEVELING  INSTRUMENT.  While  it  is 
possible  to  so  mount  the  leveling  instrument  upon  a  plat- 

122 


THE        STARRETT        BOOK 

form  that  its  height  will  be  sufficient  for  the  use  of 
targets  mounted  upon  the  shaft,  the  usual  method  is  to 
hang  targets  upon  the  shaft  and  adjust  them  to  swing  low 
enough  to  allow  the  leveling  instrument  to  be  set  with 
its  tripod  on  the  floor  or  on  some  convenient  foundation 
spot. 

THE  TARGETS.  These  consist  of  stirrups  which 
carry  a  spirit  level  and  block  with  vertical  and  horizontal 
lines  crossing  each  other.  A  plumb  is  hung  upon  the  stir- 
rup in  such  manner  as  to  be  readily  raised  or  lowered. 
One  of  the  targets  may  be  hung  upon  the  shaft  free  to 
swing  plumb,  the  other  is  used  as  a  fixed  wall  target. 

USE.  After  the  shafting  has  been  roughly  aligned 
with  the  wall  of  the  building  or  with  a  line  of  columns, 
this  being  done  by  measurement,  the  leveling  instrument 
is  placed  vertically  beneath  one  end  of  thfc  shaft.  To 
locate  the  leveling  instrument,  plumb  down  from  the 
center  of  the  shaft,  using  the  hanging  target  plumb  bob, 
and  locate  a  point  in  the  floor  or  board  placed  on  the 
foundation.  A  prick  punch  mark  in  the  flat  head  of  a 
wire  brad  previously  driven  into  the  floor  provides  a 
permanent  point.  Set  the  tripod  of  the  leveling  instru- 
ment directly  over  this  point,  using  the  plumb  bob  hang- 
ing from  the  center  of  the  table.  Next  carefully  level 
the  table  as  already  described.  Hang  the  portable  target 
closely  in  front  of  the  cross-hair  end  of  the  tube  and 
level  and  adjust  its  height  until  the  horizontal  cross  hair 
of  the  tube  coincides  with  the  horizontal  cross  line  of 
the  target. 

Remove  the  target  to  the  far  end  of  the  shaft  and 
swing  the  tube  of  the  leveling  instrument  until  the  sight 
through  the  tube  coincides  with  the  vertical  line  on  the 
target.  With  the  hanging  target  displaced,  mount  a  fixed 
target  upon  the  wall  at  the  far  end  of  the  shaft  and 
adjust  it  until  its  cross  lines  coincide  with  the  cross 
hairs  of  the  tube  as  sighted.  If  the  instrument  is  in  its 

123 


THE       STARRETT       BOOK 

original  position  with  the  plumb  bob  over  the  point  in 
the  floor,  the  setting  up  of  the  instrument  is  complete. 
By  reference  to  the  fixed  target  it  can  at  all  times  be 
checked. 

Replace  the  hanging  target  at  the  far  end  of  the  shaft 
and  adjust  the  adjacent  hanger  so  that  the  cross  lines 
of  the  target  coincide  with  the  cross  hairs  when  sight- 
ing through  the  tube.  Repeat  for  each  hanger  until  the 
target  can  be  hung  upon  the  shaft  adjacent  to  any  hanger 
and  show  perfect  coincidence  of  target  cross  lines  and 
tube  cross  hairs. 

Note  that  after  the  instrument  and  target  have  been 
set  neither  should  receive  further  adjustment  except  in 
case  of  accident  —  the  shaft  itself  receives  the  adjust- 
ments. 

HOW  TO  SET  UP  THE  TRANSIT 

The  Starrett  transit  or  level  can  be  used  for  the  same 
purposes  as  any  engineer's  transit  and  level,  and  because 
of  its  simplicity  and  freedom  from  complications,  it 
can  be  used  by  any  one  in  laying  out  foundations  for 
buildings,  aligning  machinery,  and  in  building  dams 
and  raceways  for  simple  water-power  developments. 

The  transit  combines  in  one  instrument  the  facili- 
ties for  measuring  both  horizontal  and  vertical  angles, 
and  enables  the  operator  to  lay  out  anything  that  does 
not  require  excessive  refinement.  The  level  is  for  meas- 
uring angles  in  a  horizontal  plane  only,  and  it  should  be 
borne  in  mind  that  the  level  will  do  all  that  the  transit 
will  do,  except  measure  vertical  angles.  The  transit, 
which  is  furnished  either  with  a  telescope  or  plain-sight 
tube,  is  mounted  on  a  tripod,  and  has  a  plate  carrying 
a  graduated  arc.  The  telescope  or  sight-tube  is  connected 
to  a  graduated  vertical  arc  so  that  vertical  angles  may 
be  measured  as  well  as  horizontal.  It  is  provided  with 

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THE        STARRETT       BOOK 

leveling  screws,  and  with  a  ground  level  vial  for  adjust- 
ing the  level  of  the  graduated  plate. 

To  level  the  instrument,  the  legs  must  be  firmly  set 
into  the  ground  or  floor,  so  that  neither  wind  nor  acci- 
dental touch  will  disturb  the  adjustment.  It  should  then 
be  made  as  nearly  level  as  possible  by  adjusting  the 
lower  parts  of  the  extension  legs.  It  should  then  be 
brought  to  a  perfect  level  by  means  of  the  leveling  screws 
between  the  plate  and  tripod  head.  This  is  done  by 
bringing  the  level  over  any  one  of  the  leveling  screws 
and  turning  one  screw  in  and  another  out  until  the 
bubble  appears  in  the  center  of  the  level  glass.  The  sight 
tube  or  telescope  should  then  be  turned  through  an 
angle  of  about  ninety  degrees  and  again  the  bubble  ad- 
justed to  the  center  of  the  glass  by  means  of  two  leveling 
screws.  This  operation  should  be  continued  until  the 
bubble  stands  in  the  center  of  the  glass,  no  matter  in 
what  direction  the  telescope  may  be  turned. 

To  find  differences  of  level  of  two  places,  the  instru- 
ment should  be  placed  in  a  position  about  equally  dis- 
tant from  the  two  points.  First  obtain  the  height  of 
the  target  on  one  of  the  rods  by  means  of  the  cross  line 
in  telescope  or  sight  tube  and  make  record  of  the  same. 
Then  carry  the  rod  to  the  other  position  and  find  the 
height  of  the  target  at  that  point.  The  difference  be- 
tween the  two  heights,  as  read  on  the  rod,  will  be  the 
difference  of  level  of  the  two  places,  that  place  being 
higher  at  which  the  height  of  the  target  is  less. 


125 


THE       STARRETT       BOOK 


ELEMENTARY  ALGEBRA 

Many  engineering  and  shop  problems  can  be  solved 
more  readily  with  algebra  than  by  means  of  arithmetic. 
In  fact,  some  problems  cannot  be  solved  by  arithmetic; 
as,  for  example,  when  the  conditions  are  not  fully  and 
concretely  stated.  Algebra  is  applied  by  expressing  the 
relations  in  algebraic  terms,  forming  them  into  an  equa- 
tion, which  states  the  conditions,  and  then  solving  the 
equation. 

In  arithmetic  a  figure  has  a  definite  value,  4  or  20 
for  instance,  and  the  value  remains  unchanged;  it  is 
always  4  or  20.  In  algebra  letters  are  used,  and  as  these 
letters  do  not  always  have  a  definite  value,  their  use  adds 
flexibility  to  mathematical  operations.  Some  find  it  easier 
at  the  beginning  to  think  of  the  letters  as  abbreviations. 

SYMBOLS 

Some  of  the  symbols  or  signs  of  algebra  are  the 
same  as  those  used  in  arithmetic. 

THE  SYMBOLS  OF  QUANTITY  are  the  figures  used 
in  arithmetic  and  the  letters  of  the  alphabet. 

THE  COMMON  SYMBOLS  OF  OPERATION  are  the 
signs  used  in  arithmetic;  they  are  as  follows: 

+  is  the  sign  of  addition,  called  plus.  If  no  sign 
precedes  numbers  or  letters  the  plus  sign  is  understood; 
that  is,  2abc  is  +  2abc. 

—  is  the  sign  of  subtraction,  or  difference,  called 
minus. 

X  is  the  sign  of  multiplication,  called  times.  When 
there  is  no  sign  between  letters  or  between  letters  and 
figures,  multiplication  is  understood.  Thus  Serf  means 
3  X  c  X  d.  But  this  does  not  apply  to  numbers :  328 
is  not  3  X  2  X  8,  but  328,  same  as  in  arithmetic. 

126 


THE        STARRETT       BOOK 

* 

-*-  is  the  sign  of  division,  read  "  divided  by."  Divi- 
sion may  also  be  expressed  by  a  horizontal  line  between 

a        16 

the  quantities,  as,  a  -*-  b  =  —  or  —  =  16  -*-  4. 

b         4 

COEFFICIENT.  The  numerical  factor  or  number  is 
generally  called  the  coefficient;  in  5abc,  5  is  the  coeffi- 
cient; but,  strictly  speaking,  5a  is  the  coefficient  of  be, 
and  5a&  is  the  coefficient  of  c.  Again  in  the  expression 
3a  (b  —  c),  3a  is  the  coefficient  of  (b  —  c),  or  in  the  ex- 
pression (a  +  b)  x,  (a  +  b)  is  the  coefficient  of  x. 

When  no  numerical  coefficient  is  expressed,  it  is 
always  unity  or  1.  Thus  a  =  la. 

EXPONENT.  The  small  figure  or  letter  written  at 
the  right  and  a  little  above  a  number  or  letter  is  called 
the  exponent;  it  shows  how  many  times  the  number  is 
to  be  taken  as  a  factor. 

Thus  22  is  read  "2  squared"  or  "2  with  the  exponent 
2."  The  number  2  is  to  be  used  twice  as  a  factor,  or  mul- 
tiplied by  itself.  Similarly  a3  is  read  "a  cubed"  or  "a  with 
the  exponent  3."  The  letter  a  is  to  be  taken  three  times 
as  a  factor,  or  a  X  a  X  a.  In  the  same  way  (m  +  n)4= 
(m  +  n)  X  (m  +  n)  X  (m  +  n)  X  (m  +  n). 

Again  a*bc*d*=a X aXbX  cX  cXcXdXd  XdXd. 

Note  this  difference  — 

m*=  m  X  m  X  m  X  m 
4m  =  m  +  m  +  m  +  m 

SYMBOLS  OF  RELATION  show  the  relative  values 
of  letters. 

=  is  the  sign  of  equality,  read  "equals"  or  "equal  to." 
a  =  b  means  that  a  is  equal  to  b,  or  whatever  value  is 
given  to  a,  the  same  value  must  be  given  to  b.  If  4a  =  3&, 
4  times  some  quantity  represented  by  a  is  equal  to  3  times 
some  quantity  represented  by  b,  but  it  is  evident  that  a 
does  not  equal  b. 

:  is  read  "is  to"  or  "to."    It  indicates  ratio. 

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THE       STARRETT       BOOK 

If  two  ratios  are  equal,  they  may,  01  course,  be  con- 
nected by  the  sign  of  equality,  but  more  often  they  are 
connected  by  this  sign  : : 


SYMBOLS  OF  AGGREGATION 

(  )  Parentheses. 

[  ]  Brackets. 

|   j  Braces. 

Vinculum. 

V  Radical  Sign  (square  root). 

Letters  or  quantities  enclosed  in  parentheses  are  to 
be  handled  as  a  single  quantity. 

5  (c  +  d)  means  that  c  +  d  as  one  quantity  is  to 
be  multiplied  by  5. 

Or  (a  +  b)  -5-  (x  +  {/)  means  that  a  +  b  taken  as  a 
single  quantity  is  to  be  divided  by  x  +  y  taken  as  a  sin- 
gle quantity.  Another  way  of  expressing  it  is,  the  same 
operation  performed  on  a  must  be  performed  on  b  also. 

Again  —  (a  +  b)  means  that  the  sum  of  a  and  b  taken 
as  a  single  quantity  is  to  be  subtracted.  It  does  not  mean 
that  a  alone  is  to  be  subtracted. 

THE  RADICAL  SIGN.  This  sign  is  used  as  in  arith- 
metic; that  is,  it  shows  that  some  root  of  the  quantity 
is  to  be  found,  or  expressed. 

The  small  number  or  index  used  in  connection  with 
the  radical  sign  denotes  what  root  is  meant.  Thus  ^/~a 
is  read  "the  cube  root  of  a."  ^/6  is  read  the  fifth  root 
of  ft."  When  no  index  figure  is  used  the  square  root  is 
understood.  Vx  +  y  =  the  square  root  of  x  +  y. 

When  the  horizontal  line  extends  over  the  expression 
it  means  that  the  indicated  root  is  to  be  found  of  the 
entire  expression.  V  m  +  n  =  "the  square  root  of  m  +  n." 

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THE       STARRETT       BOOK 

Let  m  =  36  and  n  =  64. 

V~m~+  n=  V"367F  64  =  VIM"  =  10 
V/n  +  n=V36+  64=6  +  64-70 
Vm  +  Vn  =  V36+  V64=6+  8  =  14 

POSITIVE  AND  NEGATIVE  TERMS 

A  term  or  quantity  preceded  by  the  plus  sign,  or  by 
no  sign  at  all,  is  a  positive  term,  and  one  preceded  by  the 
minus  sign  is  a  negative  term.  This  applies  whether  the 
term  is  a  simple  one  like  3a  (a  monomial)  or  (x  +  y) 
(a  binomial)  or  (a2  +  2ab  +  b2)  (a  polynomial). 

SIMILAR  TERMS.  When  several  terms  have  the 
same  letters,  but  may  differ  in  numerical  coefficients, 
they  are  called  similar  terms.  Thus  4ac,  —  5ac,  and  3ac 
are  similar  terms. 

In  arithmetic  we  say  that  +  5  and  —  5  cancel;  that 
is,  if  we  have  five  units  and  subtract  five  units  we  get 
zero.  Similarly  in  algebra  5a  cancels  —  5a,  or  —  Gcfxy 
cancels  Qa2xy. 

ADDITION 

Addition  is  finding  the  sum  of  two  or  more  quantities. 

Arithmetic  Algebra 

4  apples  4ab 

3  apples  3a& 

10  apples  lOafr 

17  apples  11  ab 

When  the  terms  are  alike,  we  add  them  by  adding 
the  coefficients;  when  they  are  not  alike  the  addition 
is  expressed. 

6ac  added  to 
6ac  • 

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THE       S    T    A   R   RETT       BOOK 

If  the  terms  have  different  signs  they  can  be  added 
by  algebra. 

—  6ac  added  to  ISac  =  12ac 

—  6ac  added  to  ISxy  =  I8xy  —  6ac 

When  there  are  several  quantities  which  are  alike, 
but  the  signs  unlike,  we  add  them  by  adding  all  the  posi- 
tive or  plus  terms,  then  subtract  the  sum  of  all  the  nega- 
tive or  minus  terms.  For  instance, 

5/nn 
—  2mn 


3/nn 
—  6mn 

15mn 

The  positive  terms  in  the  above  equal  +  23mn  and 
the  negative  terms  equal  —  8mn,  the  result  being 
23mn  —  8mn  =  15mn. 

Had  all  the  signs  been  changed,  the  answer  would 
have  been  —  15/nn;  for  the  sign  prefixed  to  the  answer 
is  that  of  the  greater  sum. 

SUBTRACTION 

Subtraction  in  many  ways  is  like  addition;  that  is, 
like  terms  can  be  subtracted  in  the  same  way  that  they 
can  be  added,  and  unlike  terms  are  subtracted  by  indi- 
cating the  difference. 

Subtraction  is  the  process  of  finding  the  DIFFER- 
ENCE between  two  quantities. 

In  arithmetic  the  larger  cannot  be  subtracted  from 
the  smaller,  but  in  algebra  this  can  be  done  by  express- 
ing the  difference. 

In  arithmetic  11  cannot  be  subtracted  from  4,  but 
in  algebra  7  —  11  =  —  4;  that  is,  7  lacks  4  of  being  equal 
to  11.  It  is  minus  4. 

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THE       STARRETT       BOOK 

The  difference  (in  number  of  units)  between  8  and 
2  is  6,  whether  it  is  8  —  2  or  2  —  8.  Whether  the  differ- 
ence is  —  6  or  +  6  depends  upon  which  number  is  being 
subtracted. 

These  few  rules  should  be  remembered. 

Subtracting  a  +  quantity  is  the  same  as  adding  a 
minus  quantity. 

Subtracting  a  —  quantity  is  the  same  as  adding  a 
plus  quantity. 

The  sum  of  a  minus  quantity  and  a  plus  quantity  is 
the  difference  between  the  quantities,  with  the  prefixed 
sign  of  the  larger. 

The  difference  between  a  plus  quantity  and  a  minus 
quantity  is  equal  to  the  sum  of  the  quantities. 

MULTIPLICATION 

Multiplication  is  a  short  method  of  addition;  that  is, 
if  you  add  4ac  five  times,  the  result  is  the  same  as  mul- 
tiplying 4ac  by  5. 

4ac 

4ac  4ac 

4ac  5 


20ac 


Multiplication  is  a  process  of  taking  a  given  quan- 
tity as  many  times  as  indicated  by  a  number  or  another 
quantity. 

Multiplication  differs  from  addition  in  that  unlike 
quantities  can  be  multiplied. 

5abx  multiplied  by  Qaxy  = 
131 


THE       STARRETT       BOOK 

This  simple  example  shows  that  to  multiply  we  first 
multiply  the  coefficients,  then  annex  the  letters,  multi- 
plying them  when  alike  by  adding  the  exponents;  for 
instance,  a  X  a  =  a2,  x  X  x  =  x~. 

SIGNS.  If  both  quantities  are  plus,  the  product  is 
plus;  if  both  are  minus,  the  product  is  plus;  if  one  is 
plus  and  the  other  minus,  the  product  is  minus. 

Multiplying  more  complicated  quantities,  those  con- 
sisting of  two  or  more  terms  each,  is  illustrated  by  this 
example  in  arithmetic: 

Multiply  4  +  3  +  2-1  by  6 

Instead  of  adding  before  multiplying  let  us  multiply 
each  number  by  6 : 

4+    3+    2-1 
6 


24  +  18  +  12  -  6  =  48 

If  we  use  letters  also,  we  proceed  in  the  same  way : 
Multiply  4ac  +  Sab  +  2e  —  c  by  6a. 

4ac  +    3afc  +      2c  -  c 
6a 


24a2c  +  18a2fc  +  12ac  -  6ac 
Combining  similar  terms,  24o2c  +  18a2£  +  6ac 
Multiply  2a  +  4b  by  3a  -  66 


6a2+ 


Go2  -24&' 

132 


THE        STARRETT       BOOK 

The  above  example  should  be  thoroughly  understood, 
for  it  involves  multiplication,  addition,  and  cancellation 
of  like  terms. 

If  three  quantities  are  to  be  multiplied,  first  multiply 
two  of  them,  then  multiply  the  product  by  the  third. 


DIVISION 

Division  is  the  process  of  finding  how  many  times 
one  quantity  is  contained  in  another. 

In  arithmetic  dividing  20  by  4  is  finding  how  many 
times  4  is  contained  in  20. 

In  algebra  dividing  25a2fcc  by  Sac  is  finding  how 
many  times  5ac  will  go  in  25a2£c. 

First  divide  the  coefficient  25  by  5,  then  divide  the 
letters  by  subtracting  the  exponents  of  the  same  letter, 
a2  -*-  a  =  a  because  2  —  1  =  1.  When  no  similar  letter  is 
in  the  dividend,  as  in  the  case  of  b,  there  is  no  exponent 
to  subtract,  therefore  we  put  the  b  in  the  quotient.  In 
the  case  of  the  letter  c,  c  goes  in  c  once  or  1. 


5ac  ) 

25a  c 


ab 

Another  way  to  state  this  is  to  divide  the  terms  into 
factors  : 


5ac 


=5ab 


The  5  cancels  5  in  the  numerator,  a  cancels  one  a 
in  the  numerator  and  c  cancels  c.  These  cancel  because 
the  exponents  become  zero;  for  instance,  1  —  1  =  0,  and 
c  with  the  exponent  zero  equals  one  or  unity. 

133 


THE        STARRETT       BOOK 

SIGNS.  Since  division  is  the  converse  of  multipli- 
cation, the  rules  governing  signs  are  practically  the  same : 

When  both  divisor  and  dividend  are  +  the  quotient 
is  +. 

When  both  divisor  and  dividend  are  —  the  quotient 

When  the  divisor  is  +  and  the  dividend  is  —  the 
quotient  is  — . 

When  the  divisor  is  —  and  the  dividend  is  +  the 
quotient  is  — . 

The  process  of  polynomials  is  merely  an  extension 
of  the  process  of  dividing  monomials. 

Example:  Divide  40a4  —  35a3&  +  Sa2b  —  lab2  by 
8<f  -  lab : 

So3  -  lab)  40a4-  35a3fc  +  Sa2b  -  lab2  (oa2  +  b 
40a4—  35a3fc 

8a2b  -  lab2 
Sa2b  -  lab2 

EQUATIONS 

AN  EQUATION  is  an  algebraic  expression  in  which 
two  or  more  terms  or  quantities  are  connected  by  the 
sign  of  equality.  The  two  terms  or  expressions  are  called 
members  or  sides  of  the  equation;  the  term  on  the  left- 
hand  side  is  called  the  first,  and  that  on  the  right-hand 
side  is  called  the  second  term. 

The  letter  whose  value  is  to  be  found  is  called  the 
"unknown  quantity,"  and  it  is  usual  to  represent  the  un- 
known quantity  by  the  letter  (x). 

To  solve  an  equation  is  to  find  the  value  of  the  un- 
known quantity,  either  in  terms  of  numbers  or  in  terms 
of  numbers  and  letters. 

A  very  important  fact  to  remember  about  equations  is 
that  if  the  same  operation  is  performed  on  both  sides  of 

134 


THE       STARRETt       BOOK 

the  equation  the  left-hand  side  will  still  be  equal  to  the 
right-hand  side. 

The  equation  will  continue  to  be  an  equation  if 

a.  The  same  quantity  is  added  to  both  sides. 

b.  The  same  quantity  is  subtracted  from  both  sides. 

c.  Both  sides  are  divided  by  the  same  quantity. 

d.  Both  sides  are  multiplied  by  the  same  quantity. 

e.  Both  sides  are  raised  to  the  same  power. 
/.  The  same  root  of  both  sides  is  extracted. 

This  fact  is  made  use  of  in  solving  an  equation;  for 
instance, 

So:  =  20 

Dividing  both  sides  by  5,  we  have 

x  =  4 

Again,  1/5*  =  20 
Multiplying  both  sides  by  5,  we  have 

5  X  1/5*  =  5  X  20 
*  =  100 

Before  solving  an  equation  it  is  usually  easier  to 
rewrite  or  rearrange  the  terms  so  that  x  with  its  coeffi- 
cient will  be  alone  on  the  left-hand  side.  Changing  the 
terms  from  one  side  to  the  other  is  called  "transposing." 
It  is  evident  that  in  transposing  the  truth  of  the  sign  of 
equality  must  not  be  destroyed. 

Bearing  in  mind  the  fact  that  if  the  same  operation 
is  performed  on  both  sides  of  an  equation  the  left-hand 
side  remains  equal  to  the  right-hand  side,  we  can  trans- 
pose terms. 

x  -  2a  =  b 

Adding  2a  to  both  sides,  we  have 
x  -  2a  +  2a  =  b  +  2a 
135 


THESTARRETT        BOOK 

As  —  2a  cancels  +  2a,  we  have 

x  =  b  +  2a 

We  see  from  this  that  the  2a  has  been  transposed 
from  one  side  to  the  other,  and  that  in  transposing  the 
only  thing  that  happened  to  it  was  that  its  sign  was 
changed. 

Numerous  examples  would  show  this  simple  fact  that 
to  transpose  a  quantity  from  one  side  of  an  equation  to 
the  other,  it  is  only  necessary  to  write  the  quantity  on 
the  other  side  with  its  sign  changed;  plus  changed  to 
minus  or  minus  to  plus. 

If  the  term  containing  x  is  a  fraction,  the  denom- 
inator can  be  eliminated,  so  that  x  will  be  alone,  by  mul- 
tiplying both  sides  of  the  equation  by  the  denominator. 


c~        b 

First,  combine  the  fractions  on  the  right-hand  side, 
because  they  have  the  same  denominator,  thus: 
x      m2  +  n2  —  n 


To  get  x  alone  on  the  left-hand  side,  multiply  both 
sides  by  c. 

_  c  (m2  +  n2  -  n) 

x  — 

b 

Suppose  x  is  in  the  denominator  instead  of  in  the 
numerator. 

61       * 
a  H-  b 

x~    lOc 

Multiplying  both  sides  by  x  gives 
(a  +  b)x 


10c 
136 


THE        STARRETT        BOOK 


Now  transpose  all  terms 

(a  +  b)  x 

-  =  6 
lOc 

Or  dividing  both  sides  by  -'.  -  ,  the  coefficient  of  x, 

lOc 
we  have 

(a  +  b)x        We       6  (lOc) 

_______  \x  _____  —  ____ 

lOc          a  +  b~   a  +b 
60c 

a+  b 
The  short  cut  to  the  same  result  is  to  invert  both  sides. 


x         lOc 


6       a  +  b 

Then  multiplying  both  sides  by  6, 

60c 


~ 


a  +  b 

SHOP  AND  ENGINEERING 
FORMULAS 

The  letters  which  we  have  used  are  given  a  meaning 
in  shop  and  engineering  formulas  by  assigning  to  each 
a  definite  numerical  value.  The  letters  are  connected 
by  signs  to  represent  the  conditions. 

In  a  certain  shop  one-fifth  of  the  output  is  milling 
machines,  two-thirds  is  lathes,  and  the  rest  is  twenty- 
eight  shapers.  How  many  milling  machines  and  lathes 
are  produced? 

137 


THE        STARRETT       BOOK 

If  we  let  x  represent  the  total  number  of  machines, 
x  2x 

-  equals  the  number  of  milling  machines  and  —  equals 
5  3 

x 
the  number  of  lathes.     The  total  is  equal  to  -  added  to 

5 

2x 

— ,  and  this  sum  is  added  to  28  to  equal  the  unknown 
3 
quantity  x. 

x      2x 
z=-  +  — +  28 

5       3 

Multiplying  both  sides  by  15,  the  common  denomi- 
nator, to  eliminate  the  fractions,  we  have 
15*  =    3*  +  10*  +  420 
15x  =  13*  +  420 
Transposing 

15*  -  13*  =  420 

2x  =  420 

x=2W 

x      210  2x      420 

—  = =  42  milling  machines  and  —  =  —  =  140  lathes. 

5        5  3         3 

In  designing,  formulas  are  used,  and  these  formulas 
are  in  the  form  of  equations,  the  letters  having  definite 
values.  Usually  the  values  of  all  but  one  letter  are  known 
or  assumed.  The  problem  then  is  to  find  the  numerical 
value  of  the  unknown  by  substituting  the  known  values. 
For  instance,  in  designing  keys  some  use  this  formula: 
126,000  X  H.P. 

DN 

in  which  P  =  the  total  twisting  moment  on  the  shaft, 
H.  P.  =  the  horse-power  transmitted,  D  =  diameter  of 
shaft  in  inches,  and  N  =  number  of  revolutions  of  the 
shaft  per  minute. 

138 


THE       STARRETT       BOOK 

If  20  horse-power  is  transmitted  at  a  rotative  speed 
of  40  revolutions  per  minute  and  the  shaft  is  2  inches  in 
diameter,  the  twisting  moment  is  found  by  substituting 
the  known  values  and  solving  for  P. 

126,000  X  20 
P  —  - 

2  X  40 
=  31,500 

In  finding  the  thickness  of  the  hub  of  a  pulley,  some 
designers  use  this  formula : 

T  =  .14^B~D 

in  which  T  =  thickness  of  hub  in  inches, 
B  =  width  of  face  in  inches, 
D  =  diameter  of  pulley  in  inches. 

If  the  face  is  8  inches  and  the  pulley  27  inches  in 
diameter,  we  have 

T  =  .14^8  X  27 

=  .14  X  6 

=  .84  inch  or  %  inch 


139 


THE       STARRETT       BOOK 


MENSURATION 

ANGLES.  Of  all  the  plane  figures  which  the  machin- 
ist has  to  deal  with,  the  angle  is  the  most  important,  and 
also  the  most  troublesome.  Examples  of  working  to  an 
angle  are  found  in  the  setting  of  the  compound  rest  when 
taper  turning,  setting  the  head  of  the  milling  machine 
for  milling  spiral  flutes  in  twist  drills  or  reamers,  and 
in  the  cutting  of  bevel  gears.  In  laying  out  work  the 
machinist  must  understand  the  properties  of  angles  and 
the  use  of  the  protractor,  so  that  he  may  work  to  the 
angle  that  is  wanted,  not  to  some  other  angle. 

An  angle  is  sometimes  defined  as  the  difference  in 
direction  of  two  straight  lines;  another  definition  is:  an 
angle  is  the  space  between  two  straight  lines  that  meet, 
or  would  meet  if  produced.  Angles  are  also  used  for 
measuring  rotation  or  circular  movement. 

If  a  circumference  of  a  circle  is 
drawn,  having  for  a  center  the  vertex 
of  the  angle,  the  measure  of  the  angle 
will  be  that  arc  included  between  the 
sides  of  the  angle.  Angle  A  0  B  is  meas- 
ured by  the  arc  A  B. 

The  circumference  of  the  circle  is 
divided  into  360  equal  parts,  each  called 
a  degree.  Each  degree  is  divided  into  60 
equal  parts  called  minutes.  Each  minute 
into  60  equal  parts  called  seconds.  The 
angle  A  0  B  will  be  an  angle  of  60°  if 
the  arc  A  B  is  one-sixth  of  the  circum- 
ference. 
It  makes  no  difference  what  the  radius  of  the  circle 

or  arc  may  be,  the  difference  in  direction  is  the  same, 

and  the  number  of  degrees  is  the  same. 


140 


THE       STARRETT       BOOK 

A  RIGHT  ANGLE  is  one  formed  by  two  lines  per- 
pendicular to  one  another.  The  arc  which  measures  it 
is  a  quarter  circumference  or  90°.  The  tool  most  com- 
monly used  for  measuring  a  right  angle  is  a  try-square. 
Two  right  angles  are  formed  when  a  line  so  meets  an- 
other line  that  the  two  angles  are  equal. 

AN  ACUTE  ANGLE  is  any  angle  of  less  than  90°. 

AN  OBTUSE  ANGLE  is  any  angle  of  more  than  90°. 

The  complement  of  an  angle  is  the  angle  which  must 
be  added  to  the  given  angle  to  make  a  right  angle  or  90°. 
The  complement  of  an  angle  of  37°  is  53°.  Either  of 
these  angles  is  the  complement  of  the  other. 

The  supplement  of  an  angle  is  the  angle  which  must 
be  added  to  the  given  angle  to  make  180°,  or  two  right 
angles.  The  supplement  of  an  angle  of  63°  is  1X7°.  Either 
of  these  angles  is  the  supplement  of  the  other. 

The  instrument  most  commonly  used  for  measuring 
angles  is  the  protractor.  It  may  be  in  the  form  of  the 
combination  set  (page  14),  or  the  protractor  shown  in 
the  accompanying  illustration.  The  protractor  is  a  grad- 
uated disc  on  a  fixed  blade  and  adjustable  stock.  Any 
given  angle  may  be  laid  out  or  measured  by  setting  the 
blade  at  the  desired  angle  with  the  stock.  The  angle 
shown  here  is  a  little  less  than  55°. 

To  set  the  protractor  at  an  angle  of  less  than  90°  is 
an  easy  matter,  because  the  instrument  reads  directly, 
being  graduated  from  zero  to  90°.  But  when  the  desired 
angle  is  greater"  than  90°,  the  supplement  of  the  angle 
must  be  found  and  the  protractor  set  to  the  supplement. 
Thus,  to  lay  off  an  angle  of  150°  we  first  find  the  supple- 
ment or  30°  and  set  the  protractor  at  30°.  But  the  proper 
scale  must  be  selected.  It  often  happens  that  a  protractor 
set  to  60°  actually  measures  120°.  With  the  Starrett  com- 
bination set,  all  angles  are  read  directly  because  of  the 
two  scales,  each  graduated  from  zero  to  180°. 

141 


THE        STARRETT       BOOK 


BASE 
TRIANGLE 


PROTRACTOR 

A  plane  figure  of  three  sides  —  if  all 
three  sides  are  equal  in  length  the  tri- 
angle is  equilateral  and  also  equiangular; 
that  is,  all  the  angles  are  equal. 

The  sum  of  all  three  angles  is  equal 
to  two  right  angles,  or  180°. 

Any  angle  equals  180°  minus  the  sum 
of  the  other  two. 

The  areas  of  two  triangles  are  equal  if  they  have 
equal  base  and  equal  height  or  altitude. 

If  the  three  sides  of  a  triangle  are  proportional  to 
the  corresponding  sides  of  another  triangle,  the  triangles 
are  similar  and  the  corresponding  angles  are  equal. 

If  the  angles  of  a  triangle  are  equal  to  the  corre- 
sponding angles  of  another  triangle,  the  triangles  are 
similar  and  the  corresponding  sides  are  proportional. 

The  area  of  any  triangle  =  product  of  base  and 
altitude  divided  by  2. 

142 


THE       STARRETT       BOOK 


RIGHT  TRIANGLE 


A  right  triangle  is  one  having  one 
right  angle. 

The  hypotenuse  is  the  side  opposite 
the  right  angle. 

The  square  of  the  hypotenuse  is 
equal  to  the  sum  of  the  squares  of  the 
other  two  sides. 


The  area  = 


base  X  side 


Hypotenuse  =  V  base  squared  +  side  squared. 

Base  =  V  hypotenuse  squared  —  side  squared. 
Side  =  V  hypotenuse  squared  —  base  squared. 


A  plane  figure  of  four  sides.  All 
four  angles  are  right  angles,  and  the  op- 
posite sides  are  equal  and  parallel.  The 
sum  of  all  the  angles  equals  four  right 
angles,  or  360°. 

Area  =  square  of  a  side. 

the  square  of  a  diagonal 


SQUARE 


Side  =  V  area 

=  diagonal  X  .7071 
X  1.414 
X  1.414 


Diagonal  =  V  area 
=       side 


A  plane  figure  of  four  sides.  All 
four  angles  are  right  angles,  and  the  op- 
posite sides  are  equal  and. parallel.  The 
sum  of  all  the  angles  equals  four  right 
angles,  or  360°. 

The   difference   between   a  square   and   a   rectangle 


RECTANGLE 


143 


THE       STARREST       BOOK 


TRAPEZOID 


is  that  the   adjacent  sides  of  a  square   are   equal;    the 
adjacent  sides  of  a  rectangle  need  not  be  equal. 

Area  =  product  of  two  adjacent  sides. 

Short  side  =  area  divided  by  long  side. 

Long  side  =  area  divided  by  short  side. 

Diagonal  =   V  sum  of  squares  of  adjacent  sides. 


A  plane  figure  of  four  sides,  two  of 
which  are  parallel. 

Area  =  sum  of  parallel  sides  X  one- 
half  the  altitude. 

A  regular  plane  figure  of  six  sides. 

All  the  sides  are  equal  and  all  the 
angles  are  equal.  The  sum  of  all  the 
angles  equals  720°. 

Area  =  square  of  side  X  2.598. 

Area  =  square  of  radius  of  circum- 
scribed circle  X  2.598. 

Area  =  square  of  radius  of  inscribed 
circle  X  3.464. 


Side  =  radius  of  circumscribed  circle. 
Side  =  radius  of  inscribed  circle  X  1.155. 
Radius  of  inscribed  circle  =  side  X  .866. 

A  plane  figure  bounded  by  a  curved 
line,  every  point  of  which  is  equally 
distant  from  a  point  within  called  the 
center. 

A  diameter  is  any  straight  line  pass- 
ing through  the  center  and  touching  the 
CIRCLE  circumference  at  each  end. 

Two  circles  having  equal  radii  are  equal. 
Two  circles  with  unequal  radii  vary  in  area  as  the 
squares  of  the  radii  —  the  circumferences  are  propor- 
tional to  the  radii. 


144 


THE        STARRETT       BOOK 


A  chord  is  a  straight  line  intersecting  or  touching  the 
circumference,  but  not  passing  through  the  center. 

A  chord  at  right  angles  to  a  diameter  is  divided  into 
two  equal  parts  by  the  diameter. 

Circumference  =  diameter  X  3.1416. 
Area  =  square  of  radius  X  3.1416. 
Area  —  square  of  diameter  X  .7854. 
Radius  =  circumference  -H  6.2832. 
Radius  =  V  area  -*-  3.1416. 


A  plane  figure  included  between  two 
circumferences  having  the  same  center. 

Area  =  3.1416  X  (large  radius 
squared  --  small  radius  squared). 

Area  =  .7854  X  (large  diameter 
squared  —  small  diameter  squared). 

A  plane  figure  included  between  two 
radii  and  the  arc. 

Area  =  one-half  the  radius  X  length 
of  arc. 

Area  =  .008727  X  radius  squared  X 
angle  in  degrees. 

57.296  X  length  of  arc 
Angle  =  - 


radius 
57.296  X  length  of  arc 


Radius  = 


degrees  in  angle 

Length  of  arc  =  .01745  X  radius  X  degrees  in  angle. 
A  plane  figure  bounded  by  a  curve, 
of  which  every  point  is  the  same  dis- 
tance from  two  points  on  the  longest 
axis;  that  is,  the  sum  of  the  distances 
from  any  point  to  the  foci  is  equal  to 
the  sum  of  the  distances  from  any  other 
point  to  the  foci. 


145 


THE        STARRETT       BOOK 

Area  =  3.1416  X  the  product  of  its  semi-axes. 
Area  =    .7854  X  product  of  axes. 


Circumference  (approx.)  =  3.1416 


sum  of  square  of  axes 


A  cycloid  is  a  curve  formed 
by  a  given  point  on  a  circumfer- 
ence of  a  circle  rolling  on  a 
straight  line. 

Length  of  curve  =  diameter  of  circle  X  4. 
Length  of  curve  =  radius  of  circle  X  8. 
Area  =  3  X  3.1416  X  radius  squared. 
Area  =  9.4248  X  radius  squared. 
Area  =  area  of  circle  X  3. 

An  involute  is  a  curve  traced 
by  the  end  of  a  string  as  it  un- 
winds from  a  cylinder  and  is  kept 
taut.  The  string  is  always  tangent 
to  the  cylinder.  To  draw  the  curve, 
divide  the  circumference  into  any 
number  of  equal  parts,  the  smaller 
the  number,  the  more  accurate  the 
curve.  Through  these  points  on  the 
circumference,  draw  lines  at  right 
angles  to  the  radius  and  make  the  lengths  of  these  tan- 
gents equal  to  the  actual  length  of  the  arcs.  The  curve 
drawn  through  these  points  is  an  involute. 


SOLIDS 

A    solid    having   six    faces,    each    a 
square.     All  faces  and  edges  are  equal. 
Volume  =  cube  of  edge. 
Edge  =  \/  volume. 
Total  area  =  square  of  edge  X  6. 


146 


THE        STARRETT        BOOK 


SQUARE  PRISM 


HEXAGONAL 
RIGHT 
PRISM 


REGULAR  PYRAMID 


FRUSTUM  OF  PYRAMID 


A  solid  having  a  rectangular  base 
and  rectangular  sides.  All  opposite  edges 
are  equal  and  parallel. 

Volume  =  product  of  the  three 
edges. 

Any  edge  =  volume  -*-  product  of 
other  two  edges. 

Total  area  =  area  of  base  and  top 
+  area  of  sides. 

Total  area  =  sum  of  areas  of  the  six 
faces,  all  rectangular. 

A  prism  having  for  its  base  a  regular 
hexagon,  and  bases  at  right  angles  to 
faces. 

Volume  =  2.598  X  square  of  side  of 
base  X  vertical  edge,  or  altitude. 

Lateral  area  =  side  of  base  X  ver- 
tical edge  X  6. 

Total  area  =  lateral  area  +  (5.196  X 
square  of  side  of  base) . 

A  right  pyramid  is  a  solid  having  a 
base  a  regular  polygon  and  faces  isos- 
celes triangles. 

Volume  =  one-third  altitude  X  area 
of  base. 

Lateral  area  =  perimeter  of  base  X 
one-half  slant  height. 

Slant  height  =  altitude  of  triangular 
face.  

Slant  height  =  V  vertical  edge 
squared  —  one-half  side  of  base  squared. 

A  frustum  of  a  regular  pyramid  has 
parallel  bases;  that  is,  it  is  the  lower 
portion  of  a  pyramid  cut  by  a  plane 
parallel  to  the  base. 

147 


RIGHT  CONE 


THE       STARRETT       BOOK 

Volume  =  sum  of  areas  of  the  two  bases  and  mean 
proportional  between  them  X  one-third  altitude. 

The  mean  proportional  is  equal  to  the  square  root 
of  the  product. 

Lateral  area  =  the  sum  of  the  perimeters  of  the 
two  bases  X  one-half  slant  height. 

Slant  height  =  V  square  of  edge  '—  square  of  one- 
half  difference  of  side  of  bases. 

A  right  cone  has  a  circular  base  and 
vertex  in  a  line  perpendicular  to  the 
center  of  the  base.  It  is  a  solid  of  revo- 
lution; that  is,  it  is  a  solid  figure  formed 
by  revolving  a  right  triangle  on  its  verti- 
cal side  as  an  axis. 

Volume  =  1.0472  X 
of  base  X  altitude. 

Volume  =  .2618   X 
eter  of  base  X  altitude. 

Conical  area  =   3.1416   X   radius  of 

base  X  slant  height. 

Slant  height  =  V  square  of  radius  +  square  of  altitude. 
Altitude  =  V  square  of  slant  height  — square  of  radius. 

The  frustum  of  a  cone  has  parallel 
bases.  It  is  the  lower  portion  of  a  cone 
when  cut  by  a  plane  parallel  to  the  base. 
Volume  =  one-third  altitude  X  sum 
of  the  areas  of  the  two  bases  and  the 
mean  proportional  between  the  two 
bases. 

The  mean  proportional  is  equal  to  the  square  root 
of  the  product. 

Lateral  area  =  sum  of  perimeters   (circles)   of  two 

bases  X  one-half  slant  height. 

Slant  height  =  V  square  of  altitude  +  square  of 
difference  in  radii. 


square  of  radius 
square  of  diam- 


FRUSTUM   OF  CONE 


148 


THE       STARRETT       BOOK 


A  right  cylinder  is  a  solid  having 
circles  for  bases  and  lateral  surface  per- 
pendicular to  bases.  It  is  a  solid  of  revo- 
lution; that  is,  it  is  generated  by  revolv- 
ing a  rectangle  about  a  side  as  an  axis. 

Volume  =  3.1416  X  square  of  radius 
X  altitude. 

Volume  =  .7854  X  square  of  diam- 
eter X  altitude. 

Cylindrical  surface  =  6.2832  X  radius  X  altitude. 
Cylindrical  surface  =  3.1416  X  diameter  X  altitude. 

Total  surface  —  cylindrical  surface  +  twice  area  of 
(circle)  base. 


Hollow  cylinder;  axis  of  hole  coin- 
ciding with  axis  of  cylinder. 

Volume  =  difference  in  volume  of 
two  cylinders. 

Volume  =  3.1416  X  altitude  X  (square 
of  large  radius  —  square  of  small  radius). 

Volume  =  3.1416  X  altitude  X  thick- 
ness X  (large  diameter  —  thickness). 

A  sphere  is  a  solid  bounded  by  a 
curved  surface  every  point  of  which  is 
equally  distant  from  a  point  within,  called 
the  center.  It  is  a  solid  of  revolution; 
that  is,  it  is  generated  by  revolving  a  half 
circle  on  the  diameter  as  an  axis. 

4  X  3.1416  X  cube  of  radius 


HOLLOW    CYLINDER 


SPHERE 


Volume  = 


Radius  = 


=  4.1888  X  cube  of  radius 
T/ volume 


4.1888 

=  .6204  X  \j/  volume. 

149 


THE        STARRETT       BOOK 


Area  =  4  X  3.1416  X  square  of  radius, 
=  12.5664  X  square  of  radius. 


Radius  = 


area 


12.5664 

=  3.5447  X  V  area 

Hollow  sphere. 

Volume  =  difference  in  volumes  of  two  spheres. 
Volume  =  4.1888  X   (cube  of  large  radius  —  cube  of 
small  radius). 

A  spherical  segment  is  formed  by 
passing  a  plane  through  a  sphere.  If  the 
plane  passes  through  the  center,  the  seg- 
ment is  one-half  the  sphere.  If  it  does 
not  pass  through  the  center  — 

Volume  =  3.1416  X  square  of  height 
X  (radius  —  one-third  height). 

Radius  of  segment  =  V  height  X  (dia- 


SPHERICAL    SEGMENT 


SPHERICAL   ZONE 


meter  of  sphere  —  height  of  segment). 

Surface  of  spherical  segment  =  2  X 
3.1416  X  radius  of  sphere  X  height. 

Surface  of  spherical  segment  = 
6.2832  X  radius  of  sphere  X  height. 

A  spherical  zone  is  formed  by  pass- 
ing two  parallel  planes  through  a  sphere. 

Volume  =  volume  of  sphere  —  vol- 
ume of  segment. 

Area  =  2  X  3.1416  X  radius  of 
sphere  X  height. 

Area  =  6.2832  X  radius  of  sphere  X 
height. 


150 


THE       STARRETT       BOOK 
MECHANICS 

A  FORCE  is  any  cause  which  tends  to  produce  or 
modify  motion.  It  is  measured  in  pounds,  usually.  Force 
has  three  characteristics  —  direction,  place  of  applica- 
tion, magnitude. 

WORK  is  the  product  of  force  and  distance.  It  is 
measured  in  foot-pounds  or  in  inch-pounds.  Work  does 
not  involve  the  element  time. 

POWER  is  the  amount  of  work  done  in  a  given  time. 
It  is  the  product  of  force  and  distance  divided  by  time; 
and  is  expressed  in  foot-pounds  per  minute,  or  foot- 
pounds per  second.  The  element  of  time  is  always 
included. 

Power  should  not  be  given  the  same  meaning  as  force, 
although  some  carelessly  refer  to  an  applied  force  as 
being  a  power. 

VELOCITY  is  rate  of  motion.  It  is  distance  divided 
by  time,  and  is  expressed  in  feet  per  minute  or  feet  per 
second.  Velocity  does  not  include  force  nor  weight. 

MOMENT  OF  FORCE.  The  moment  of  a  force  is 
the  force  multiplied  by  the  perpendicular  distance  from 
the  fixed  point  to  the  direction  of  the  force.  The  fixed 
point  is  called  the  center  of  moments,  and  the  perpendic- 
ular distance  is  called  the  lever  arm  of  the  force.  Moment 
of  force  is  measured  in  foot-pounds  or  inch-pounds. 

GRAPHICAL  REPRESENTATION  OF  FORCES.  A 
force  may  be  represented  graphically  by  a  straight  line, 
the  length  being  proportional  to  the  magnitude.  That  is, 
the  line  is  drawn  to  some  scale.  One  end  of  the  line 
represents  the  point  of  application,  and  an  arrow  head 
at  the  other  end  represents  the  direction. 

Two  or  more  forces  may  act  together  on  a  body. 

To  find  a  single  force  which  produces  the  same  effect 
as  two  or  more  forces,  is  to  find  the  RESULTANT.  The 
operation  is  called  the  COMPOSITION  OF  FORCES. 

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THE        STARRETT        BOOK 


To   find   two   or   more   forces   which   combined   are 
equivalent  to  a  given  force  is  to  find  the  COMPONENTS. 
The  operation  is  called  the  RESOLUTION  OF  FORCES. 
PARALLELOGRAM  OF  FORCES.     When  two  forces 
acting  at  a  point  can  he  represented  in 
» direction  and  magnitude  by  the  adjacent 
sides   of   a   parallelogram,   the   resultant 
will  be  represented  in  direction  and  mag- 
nitude by  the  diagonal  of  the  parallelo- 
gram.    A  B  and  A  C  are  the  forces  and 
A  R  the  resultant. 

If  two  forces  act  in  the  same  direction,  the  resultant 
is  equal  to  their  sum. 

If  two  forces  act  in  opposite  directions,  the  resultant 
is  their  difference. 

PARALLEL  FORCES.  When  two 
forces  are  parallel  and  act  in  the  same 
direction,  but  not  from  the  same  point, 
their  resultant  is  parallel  to  both,  and  is 
equal  to  their  sum.  The  resultant  is 
located  between  the  forces  at  a  point  that 
divides  the  line  joining  the  points  of 
application  inversely  as  the  magnitudes. 
CD  : AB  =  AE  :  E  C 

If  the  forces  act  in  opposite  direc- 
tions, the  resultant  is  parallel  to  both, 
but  is  located  outside  of  them  on  the 
line  (produced)  joining  the  points  of 
application.  It  is  nearer  the  greater  force 
and  takes  the  same  direction  as  the 
greater  force,  but  in  intensity  it  is  equal 
to  the  difference  between  the  compo- 
nents. The  point  of  application  of  the 
resultant  is: 

AB  :  CD  =  CE  :  AE 


-^B 


152 


THE     STARRE'TT     BOOK 
LEVERS 

Moments  of  forces  are  very  important  factors  in 
machines.  They  may  be  illustrated  in  levers. 

A  lever  is  an  inflexible  rod,  which  may  move  about 
a  fixed,  point  called  the  fulcrum.  The  lever  arms  are  the 
portions  between  the  weights  or  forces  and  the  fulcrum. 
To  solve  all  problems  relating  to  the  lever,  it  must 
be  remembered  that  the  moments  are  the  weights  or 
forces  multiplied  by  the  distances  from  the  fulcrum; 
that  is,  by  the  lever  arms. 

As  the  lever  is  considered  in  balance,  the  product  of 
the  weight  and  length  of  weight  arm  is  equal  to  the 
product  of  the  power  and  length  of  power  arm. 

^  When   the   fulcrum   is   between   the 

f L       A    *  ~"1  weight  and  the  force,  and  both  weight 
(w)  [  and  force  act  in  the  same  direction : 

W  X  L  =  F  X  / 
or  W  :  F  =  /  :  L 

FX  I  FX  Z 

W= 


L  W 

WX  L  WX  L 

/  — 

—  i  — 


Z  F 

When  the  weight  or  load  is  between 
the  fulcrum  and  the  point  at  which  the 
force  is  applied,  the"  same  principles 
apply;  in  fact,  the  same  formulas  are 
used. 

j«— Z-*  In  the  third  form  of  lever,  the  force 

* A i    is  applied  at  a  point  between  the  fulcrum 

I  (w)  and  the  weight.    The  same  formulas  are 

used. 

If  the  weight  of  the  lever  itself  is  to  be  considered, 
the  moment  of  force  (F  X  Z)  remains  the  same,  but  there 

153 


THE       STARRETT       BOOK 


are  then  several  moments  of  weight.  The  additional 
moments  of  weight  are  found  by  multiplying  the  weight 
of  the  lever  arm  by  the  distance  of  its  center  of  gravity 
from  the  fulcrum.  In  a  lever  of  the  first  class  there  will 
be  two  moments  of  weight  due  to  the  weight  of  the  lever, 
one  will  act  with  the  moment  of  force  and  the  other  act 
with  the  moment  of  weight.  With  levers  of  the  second 
and  third  class,  the  additional  moment  of  weight  will 
act  with  the  original  moment  of  weight,  and,  therefore, 
is  added  to  it. 

THE  WINDLASS.  The  moment  of 
force  and  the  moment  of  weight  are  the 
means  for  finding  the  force  required  to 
lift  a  weight  by  a  rope  wound  on  the 
drum  of  a  windlass. 

F  X  L  =  WX  / 
WX  I 

p  __  _ 


PULLEYS  OR  BLOCKS.  The  force 
required  to  lift  the  weight  is  equal  to 
the  weight  divided  by  the  number  of 
ropes  that  are  shortened. 

W 

F  =  — 
N 

If  there  are  five  ropes  and  the  weight 
is  300  pounds,  the  force  is: 

300 
F  =  --  =  60  pounds 

o 

The  velocity  with  which  the  weight 
is  raised  is  equal  to  the  velocity  of  the 
force  divided  by  the  number  of  ropes 
shortened. 

Velocity  of  F 
Velocity  =  - 


N 


154 


THE        STARRETT       BOOK 

PULLEYS 

A  simple  way  to  transmit  power,  either  at  the  same 
speed,  or  a  change  of  speed,  is  to  place  a  pulley  on  the 
driving  shaft  and  another  on  the  driven  shaft  and  pass 
an  endless  belt  over  them.  It  is  evident  that  the  linear 
speed  of  the  pulleys  is  the  same;  that  is,  one  revolution 
of  the  driving  pulley  pulls  the  belt  through  a  distance 
equal  to  its  circumference,  and  a  point  on  the  periphery 
of  the  driven  pulley  will  be  pulled  through  this  distance 
whether  or  not  the  periphery  is  equal  to  the  circumfer- 
ence of  the  driving  pulley. 

To  change  the  rotative  speed  of  shafts  it  is  only 
necessary  to  place  on  them  pulleys  of  unlike  diameters. 

The  revolutions  are  inversely  proportional  to  the 
circumferences  and,  therefore,  to  the  diameters.  The 
smaller  pulley  runs  at  the  higher  rotative  speed. 

D  =  diameter  of  driver, 
d  =  diameter  of  driven. 

Revs,  of  driven  :  Revs,  of  driver  =  D  :  d. 
Revs,  of  driven  X  d  =  Revs,  of  driver  X  D. 

The  product  of  the  revolutions  and  diameter  of  one 
pulley  is  equal  to  the  product  of  the  revolutions  and 
diameter  of  the  other  pulley. 

From         Revs,  of  driven  X  d  =  Revs,  of  driver  X  D 

Revs,  of  driver  X  D 
we  have  d  =  — 

Revs,  of  driven 

Revs,  of  driven  X  d 
and  D  =  - 

Revs,  of  driver 

To  find  the  diameter  of  the  driven  pulley,  multiply 
the  revolutions  of  the  driver  by  its  diameter  and  divide 
by  the  revolutions  of  the  driven. 

156 


THE        STARRETT        BOOK 


Example:  The  driving  shaft  makes  150  revolutions 
per  minute  and  the  driving  pulley  is  12  inches  in  diam- 
eter. The  driven  shaft  is  to  make  600  revolutions;  what 
diameter  pulley  should  be  selected? 

150  X  12 

d  =  —  —  =  3  inches 

600 

The  driving  shaft  makes  200  revolutions  and  the 
driven  shaft  is  to  make  150  revolutions  per  minute. 
With  a  driven  pulley  of  24  inches  diameter,  what  size 
driver  pulley  should  be  used? 

150  X  24 

D  =  -  -  =  18  inches 

200 

To  find  speeds  when  sizes  of  pulleys  are  known : 
Revs,  of  driver  X  D  =  Revs,  of  driven  X  d. 
Revs,  of  driven  X  d 


Revs,  of  driver  = 


D 

Revs,  of  driver  X  D 
Revs,  of  driven  =  - 

d 

Example:  The  driver  pulley  is  16  inches  diameter 
and  the  driven  is  18  inches  diameter.  When  the  driver 
runs  at  270  revolutions  per  minute,  what  will  be  the  speed 
of  the  driven  pulley? 

156 


THE        STARRETT        ROOK 

Revs,  of  driver  X  D 


Revs,  of  driven  = 


270  X  16 

-=240 
18 

Example:  Two  pulleys,  one  of  14  inches  diameter 
and  the  other  of  18  inches  diameter,  are  available.  The 
driven  shaft  is  to  run  at  120  revolutions  per  minute.  If 
the  14-inch  pulley  is  placed  on  the  driven  shaft  what 
should  be  the  speed  of  the  driver? 

Revs,  of  driven  X  d 
Revs,  of  driver  =  — 


D 

120  X  14 


18 


=  93  1-3 


FORMULAS  FOR  PULLEY  DIAMETERS  AND 
REVOLUTIONS 

When   three  factors   are  known  the  fourth  can  be 
found  by  using  one  of  the  following  formulas: 

Dia  of  driven   X   Revs,  of  driven 

Dia.  of  Driver     = 

Revs,  of  driver 

Dia.  of  driver  X  Revs,  of  driver 


Dia.  of  Driven  =• 
Revs,  of  Driver  = 
Revs,  of  Driven  =• 


Revs,  of  driven 
Dia.  of  driven  X  Revs,  of  driven 

Dia.  of  driver 
Dia.  of  driver  X  Revs,  of  driver 

Dia.  of  driven 
167 


THE        STARRETT       BOOK 

The  same  principles  apply  to  more  complex  belting. 
Suppose  two  pulleys  are  on  the  same  shaft;  we  then 
have  a  combination  that  resembles  a  train  of  gears. 

This  arrangement  is  often  desirable  when  it  is  im- 
practicable to  get  the  speed  reduction  with  one  belt; 
that  is,  when  the  larger  pulley  would  have  to  be  very 
large  as  compared  with  the  smaller. 


In  the  above  illustration  the  high  rotative  speed  of 
pulley  A  (on  a  motor  shaft  for  example)  is  reduced  to 
a  much  lower  figure  at  pulley  D. 

Revs,  of  A  X  diameter  of  A  =  Revs,  of  B  X  diameter 
of  B  and  Revs,  of  C  X  diameter  of  C  =  Revs,  of  D  X  diam- 
eter of  D.  But  pulleys  B  and  C  are  on  the  same  shaft  and 
have  the  same  rotative  speed. 

Revs,  of  B  =  Revs,  of  C. 

Combining  these  equations  we  may  express  the  rela- 
tion as  follows: 

The  speed  of  the  first  driver  multiplied  by  the 
diameters  of  all  the  drivers  is  eqaal  to  the  speed  of  the 
last  driven  pulley  multiplied  by  the  diameters  of  all 
driven  pulleys.  Or 

Revs,  of  A  X  diameter  of  A  X  diameter  of  C  = 
Revs,  of  D  X  diameter  of  B  X  diameter  of  D. 

If  five  of  the  above  quantities  are  known  the  sixth 
is  easily  found. 

168 


THE        STARRETT       BOOK 

Example:  Pulley  A  runs  at  1200  Rev.  per  minute, 
and  is  4  inches  in  diameter.  Pulley  B  is  12  inches  in 
diameter,  C  is  5  inches,  and  D  is  16  inches.  What  is 
the  speed  of  D? 

1200   X   4   X   5  =  Revs,  of  D   X   12   X    16 
24,000  =  Revs,  of  D  X   192 

24,000 

Revs,  of  D  = 

192 

=      125 

In  the  above  we  have  found  the  rotative  speed  of  D 
without  finding  the  rotative  speed  of  B,  but  we  had  given 
the  diameters  of  B  and  C. 

Suppose  we  had  given  the  speed  of  D.  J>ut  do  not 
know  what  pulleys  to  use  in  place  of  B  and  G. 

Revs,  of  first  driver      product  of  diameters  of  all  drivens 
Revs,  of  last  driven      product  of  diameters  of  all  drivers 
Revs,  of  A      diameter  of  B  X  diameter  of  D 


or 


Revs,  of  D      diameter  of  A  X  diameter  of  C 


The  two  unknown  quantities  are  diameter  of  B  and 
diameter  of  G;  but  the  RATIO  can  be  found.  Using  the 
data  in  the  above  example  we  have 

1200      16  X  diameter  of  B 


125       diameter  of  C  X  4 
Diameter  of  B       4       1200 


Diameter  of  G      16        125 

-12 
~!> 

169 


THE       STARRETT       ROOK 

Then  the  ratio  of  the  diameters  is  12  :  5,  and  any 
pulleys  having  diameters  in  this  ratio  will  give  the  desired 
speeds.  The  pulleys  may  be  12  and  5  inches,  18  and  7V2, 
or  24  and  10. 

Example:  The  shaft  of  3-inch  pulley  D  is  to  make 
900  revolutions;  what  pulleys  must  be  placet  as  B  and 


C  if  A  is  14  inches  in  diameter  and 
makes  150  revolutions?  The  available 
pulleys  have  these  diameters  —  8,  9, 
10V2,  11,  12,  13y2  inches. 

The  formula  to  use  is 

Revs,  of  first  driver      product  of  diameters  of  all  drivens 

Revs,  of  last  driven      product  of  diameters  of  all  drivers 

150      diameter  of  B  X  3 


900      14  X  diameter  of  C 
1         3       diameter  of  B 

^Tijn      _    vv 

6        14      diameter  of  C 


Diameter  of  B       1       14 

__   vx     f_ 

Diameter  of  C       6        3 
_14_   7 
~18~  "9" 
160 


THE       STARRETT       BOOK 

Then  multiply  the  ratio  7  :  9  by  any  number  which 
will  make  7  and  9  equal  to  the  diameters  of  pulleys  on 
hand.  Multiplying  by  1%  gives  10%  and  13y2. 

To  prove  that  the  calculation  is  correct,  place  these 
values  in  this  expression: 

The  speed  of  the  first  driver  (150)  multiplied  by  the 
diameters  of  all  drivers  (14)  and  (13%)  is  equal  to  the 
speed  of  the  last  driven  (900)  multiplied  by  the  diam- 
eters of  all  driven  pulleys  (10%)  and  (3). 

150  X  14  X  13%  =  900  X  10%  X  3 
28,350  =  28,350 

LENGTH  OF  BELTS 

Open  Belt.  Pass  a  tape,  preferably  a  steel  tape, 
around  the  pulleys.  This  will  give  the  length  direct,  if  a 
single  belt;  but  if  a  double  belt  is  to  be  used  add  to  the 
measurement  twice  the  thickness  of  the  belt.  The  length 
of  small  belts  may  be  obtained  by  passing  the  belt  around 
the  pulleys  and  straining  with  hand  pull. 

New  belts  stretch  and  become  slack  after  a  short 
time,  and  the  slack  should  be  taken  up.  With  long  belts 
stretching  may  be  anticipated  by  cutting  the  belt  one 
inch  shorter  for  every  ten  feet. 

Rule  for  Length  of  Open  Belt 

Add  diameters  of  pulleys  in  inches  and  multiply  the 
sum  by  1.57,  then  add  to  this  product  twice  the  distance 
between  centers  in  inches. 

Formula  for  Length  of  Open  Belt 

(R-r)2 
L  =  3.14  (R+r)  +2D  +  - 

D 

R  =  Radius  of  large  pulley,  inches. 

r  =  radius  of  small  pulley,  inches. 

D  =  Distance  between  centers  of  shaft,  inches. 

L  =  Length  of  belt,  inches. 

161 


THE        S-TARRETT        BOOK 

Formula  for  Length  of  Crossed  Belt 

(R  +  r)2 
L  =  3.14  (R  +  r)  +  2D  + 

D 

The  letters  have  the  same  values  as  above. 

Example:  Two  pulleys  are  11  feet  apart  and  are  24 
and  16  inches  in  diameter.  Length  of  belt?  Open  and 
crossed. 

(12-  8)* 
L  =  3.14  X  (12  +  8)  +  (2  X  132)  +  - 

132 

16 

=  62.8  +  264  +  - 
132 

=  326.8  +  .12 

=  326.92  inches,  open  belt. 

-(12  +  8)2 
L  =  3.14  X  (12  +  8)  +  (2  X  132)  +  - 

132 

400 
=  62.8  +  264  +  - 

132 

=  326.8  +  3 

=  329.8  inches,  crossed  belt. 

GEARS 

CONSTANT  VELOCITY  RATIO.  Belts  over  pulleys 
and  plain  rolling  cylinders  cannot  be  depended  upon 
to  give  a  constant  velocity  ratio  —  there  is  always  some 
loss  of  speed  due  to  slip.  But  when  two  gears  are  in 
mesh  a  point  on  the  pitch  circle  of  one  moves  at  the 
same  linear  velocity  as  a  point  on  the  pitch  circle  of 
the  other,  and  the  number  of  revolutions  is  always  a 
constant  ratio  for  these  two  gears. 

162 


THE        STARRETT       BOOK 

Two  gears  in  mesh  have  the  same  pitch;  that  is,  the 
distance  from  the  center  of  a  tooth  to  the  center  of  the 
next  tooth,  measured  along  the  pitch  circle,  is  the  same 
for  both  gears.  Therefore,  two  gears  of  the  same  pitch, 
but  of  different  diameters,  must  have  an  unequal  number 
of  teeth. 

It  may  be  said  that  the  space  occupied  by  a  tooth 
and  the  space  between  two  teeth  is  the  same  in  both 
gears  if  they  have  the  same  pitch.  This  fact  shows 
immediately  that  the  linear  velocity  of  the  pitch  circles 
must  be  equal  and  the  rotative  speeds  can  be  found  in  the 
same  way  as  with  belts.  The  pitch  diameter  or  the  num- 
ber of  teeth  is  substituted  for  the  pulley  diameter,  for 
the  numbers  of  teeth  are  proportional  to  the  pitch  diam- 
eters in  the  same  way  that  the  peripheries  of  pulleys  are 
proportional  to  the  diameters. 

A  gear  having  twice  as  many  teeth  as  the  gear  mesh- 
ing with  it  will  make  but  one-half  as  many  revolutions 
in  a  given  time.  Or,  the  speeds  (rotative)  are  inversely 
as  the  number  of  teeth;  the  gear  with  the  smaller  number 
of  teeth  runs  at  the  higher  speed. 

As  in  belts  and  pulleys,  one  gear  of  a  pair  is  the 
driver  and  the  other  the  driven  or  follower. 

The  number  of  revolutions  of  the  driver  multiplied 
by  the  number  of  teeth  on  the  driver  is  equal  to  the 
number  of  revolutions  of  the  follower  multiplied  by  the 
number  of  teeth  on  the  follower. 

Revs,  of  driver  X  T  =  Revs,  of  follower  X  t,  if 
T  =  number  of  teeth  on  the  driver  and  t  =  number  of 
teeth  on  the  follower: 

"Revs,  of  follower  X  / 
T  = 


and      t  = 


Revs,  of  driver 
Revs,  of  driver  X  T 
Revs,  of  follower 
163 


THE       STARRETT       BOOK 

To  find  the  number  of  teeth  (T)  on  the  driver,  mul- 
tiply the  revolutions  of  the  follower  by  its  number  of 
teeth  and  divide  the  product  by  the  revolutions  of  the 
driver. 

Example:  The  follower  has  64  teeth  and  makes  30 
revolutions  per  minute.  The  driver  makes  80  revolutions 
per  minute.  How  many  teeth  has  the  driver? 

30  X  64 

T  =  -         -  =  24 
80 

Example:  The  driver  makes  160  revolutions  per 
minute  and  has  40  teeth.  The  follower  makes  100  revo- 
lutions. How  many  teeth? 

160  X  40 

/  =  -  -  =  64 

100 

Revs,  of  follower  X  / 
Revs,  of  driver  =  - 


Revs,  of  follower  = 


T 
Revs,  of  driver  X  T 


Example:  The  follower  has  90  teeth  and  makes  110 
revolutions  per  minute.  If  the  driver  has  44  teeth,  how 
many  revolutions  per  minute? 

110  X  90 

Revs,  of  driver  =  —         -  =  225 
44 

Example:  A  driver  having  63  teeth  makes  800  revo- 
lutions per  minute.  If  the  follower  has  42  teeth,  what 
will  be  its  speed? 

800  X  63 

Revs,  of  follower  =•—  —  =  1200 

42 

164 


THE        STARRETT       BOOK 


FORMULAS  FOR  SPEED  OF  GEARS 

When  three   factors  are  known  the   fourth  can  be 
found  by  using  one  of  the  following  formulas: 

Revs,  of  follower  X  teeth  on  follower 
Revs,    of    Driver  =  — 


Revs,  of  Follower  = 


teeth  on  driver 
Revs,  of  driver  X  teeth  on  driver 

teeth  on  follower 


Revs,  of  follower  X  teeth  on  follower 
Teeth  on  Driver  = 


Teeth  on  Follower  = 


Revs,  of  driver 
Revs,  of  driver  X  teeth  on  driver 

Revs,  of  follower 


As  in  the  case  of  pulleys,  great  speed  changes  are 
made  by  trains  of  gears  in  place  of  a  pair.  Examples 
are  found  in  hoists,  clocks,  lathes,  etc.  Each  pair  in  the 
train  has  its  driver  and  follower,  and  if  the  shafts  are 
parallel  it  is  usual  to  get  the  speed  change  by  keying 
two  gears  of  unequal  size  on  every  shaft,  except  the  first 
and  last. 

The  velocity  ratio  of  the  first  to  the  last  is  found 
as  follows: 

The  product  of  the  number  of  teeth  on  all  the  drivers 
divided  by  the  product  of  the  number  of  teeth  on  all  the 
followers  is  the  velocity  ratio. 

Suppose  the  train  has  three  drivers,  A,  B,  and  C  and 
three  followers,  L,  M,  and  N. 

A  has  14  teeth  and  drives  L  having  70  teeth.  Pinion 
B  on  same  shaft  with  L  has  13  teeth  and  drives  M  hav- 
ing 104  teeth.  Pinion  C  has  15  teeth,  and  is  on  the  same 
shaft  with  M;  C  drives  N  having  75  teeth.  What  is  the 
velocity  ratio  of  A  to  N? 

165 


THE        STARRETT        BOOK 


Velocity  ratio  = 


teeth  on  A  X  teeth  on  B  X  teeth  on  C 

teeth  on  L  X  teeth  on  M  X  teeth  on  N 
14  X    13  X  15 


70  X  104  X  75 
1 

~  200 

Knowing  the  velocity  ratio  of  the  train,  it  is  easy  to 
find  the  speed  of  N  if  the  speed  of  A  is  known.  If  A 
runs  at  1800  revolutions  per  minute,  N  will  make  only 
9  revolutions  for  1800  4-  200  =  9. 

When  the  speed  of  the  first  driver  or  the  last  fol- 
lower is  also  known,  the  speed  may  be  figured  from  the 
following: 

Multiply  the  revolutions  per  minute  of  the  first  driver 
by  the  continued  product  of  the  number  of  teeth  on  all 
drivers,  and  divide  by  the  continued  product  of  the 
teeth  on  all  followers.  The  quotient  will  be  the  revolu- 
tions per  minute  of  the  last  follower. 

LATHE  GEARING 

The  apprentice  who  wishes  to  figure  change  gears 
for  screw  cutting  should  understand  the  principles,  as 

166 


THE        STARRETT       BOOK 

already  explained,  rather  than  be  dependent  upon  formu- 
las. There  is  but  one  statement  to  be  memorized. 

The  continued  product  of  the  speed  of  the  first 
driver  and  the  number  of  teeth  on  all  drivers,  is  equal 
to  the  speed  of  the  last  follower  multiplied  by  the  con- 
tinued product  of  the  teeth  on  all  followers. 

In  figuring  change  gears,  the  number  of  threads  per 
inch  to  be  cut  corresponds  to  the  revolutions  of  the 
driver,  and  the  number  of  turns  on  the  lead  screw  to 
move  the  carriage  one  inch  corresponds  to  the  speed  of 
the  follower. 

Then  the  number  of  threads  to  be  cut  multiplied  by 
the  teeth  on  the  spindle  stud  equals  the  number  of 
threads  on  the  lead  screw  multiplied  by  the  teeth  on 
the  lead  screw  gear.  Or 

threads  to  be  cut  teeth  on  lead  screw  gear 

threads  on  lead  screw      teeth  on  spindle  stud 

Suppose  there  are  6  threads  on  the  lead  screw  and 
46  teeth  on  the  lead  screw  gear  —  how  many  threads  will 
be  cut  if  a  24-tooth  gear  is  placed  on  the  spindle  stud? 

threads  to  be  cut      40 

6  "  24 

40 

threads  to  be  cut  =  —  X  6 
24 

=  10 

The  above  assumes  that  the  lathe  is  geared  1:1;  that 
is,  the  lathe  screw  constant  is  equal  to  the  number  of 
threads  per  inch  on  the  lead  screw.  If  the  lathe  is  not 
so  geared,  the  lathe  screw  constant  should  be  used  in 
place  of  the  threads  per  inch  on  the  lead  screw. 

167 


THE        STARRETT        BOOK 


The  foregoing  example  shows  how  the  figuring  can 
be  done  when  the  gears  are  on  the  spindle  stud  and  lead 
screw;  but  the  problem  is  usually  one  of  finding  out  what 
gears  to  use. 

Suppose  seven  threads  are  to  be  cut,  and  there  are 
five  threads  per  inch  on  the  lead  screw.  What  gears 
are  to  be  used? 

threads  to  be  cut  teeth  on  lead  screw  gear 

threads  on  lead  screw      teeth  on  stud  gear 

7       teeth  on  lead  screw  gear 

5       teeth  on  stud  gear 

The  ratio  of  the  gears  is  as  7  :  5. 

By  multiplying  both  7  and  5  by  any  number,  such 
as  6,  we  get 

42      teeth  on  lead  screw  gear 
30      teeth  on  stud  gear 

Using  the  formula  as  above  may  aid  in  disposing  of 
that  troublesome  question,  "Which  gear  goes  on  the 
stud?" 

In  some  cases  it  may  seem  easier  to  assume  one 
gear  and  go  through  the  calculation  to  find  the  other, 
there  being  then  one  unknown  quantity  and  three  known 
quantities. 


168 


THE        STARRETT        BOOK 


Table  13 
Specific  Gravity  and  Properties  of  Metals 


Metal  or  Composition 

Specific 
Gravity 

Weight  per 
Cubic  Inch, 
Pounds 

Melting 
Point. 
Deg.  F. 

Linear  Ex- 
pansion per 
Unit  Length 
per  Deg.  F. 

Aluminum  
Antimony  
Barium  
Bismuth  
Boron  
Brass:  80  C.,  20  Z  
70  C.,  30Z...»... 
60C..40Z  
50C..50Z  

2.56 
6.71 
3.75 
9.80 
2.60 
8.60 
8.40 
8.36 
8.20 
885 

0.0924 
0.2422 
0.1354 
0.3538 
0.0939 
0.3105 
0.3032 
0.3018 
0.2960 
03195 

1200 
1150 
1560 
500 

1700-1850 
1675 

0.00001234 
0.00000627 

0.00000975 

0.00000957 
0  00000986 

8  60 

03105 

610 

1  57 

0  0567 

1450 

Chromium  
Cobalt  
Copper  
Gold  
Iridium  
Iron,  cast  
Iron,  wrought  
Lead  

6.50 
8.65 
8.82 
19.32 
22.42 
7.20 
7.85 
11.37 
1  74 

0.2347 
0.3123 
0.3184 
0.6975 
0.8094 
0.2600 
0.2834 
0.4105 
0  0628 

2740 
2700 
1940 
1930 
4100 
2300 
2900 
620 
1200 

0.00000887 
0.00000786 
0.00000356 
0.00000556 
0.00000648 
0.00001571 

Manganese 

742 

0  2679 

2200 

Mercury  (60°  F  ) 

13  58 

04902 

—  39 

Molybdenum  
Nickel  
Platinum,  rolled  
Platinum,  wire  

8.56 
8.80 
22.67 
21.04 
0  87 

0.3090 
0.3177 
0.8184 
0.7595 
00314 

4500 
2600 

|      3200 
144 

0.00000695 
0.00000479 

Silver 

1053 

0  3802 

1740 

0  00001079 

Sodium  
Steel  
Tellurium  

0.98 
7.80 
625 

0.0354 
0.2816 
02256 

200 
2500 
840 

0.00000636 

Tin  

729 

02'632 

446 

0  00001163 

Titanium 

354 

0  1278 

3360 

18  77 

0  6776 

5400 

Vanadium  
Zinc,  cast  
Zinc,  rolled  

5.50 
6.86 
715 

0.1986 
0.2476 
02581 

3200 
|        785 

0.00001407 

169 


THE        STARRETT       BOOK 


Table  14 
Average  Specific  Gravity  of  Miscellaneous  Substances 


Substance 


Specific 
Gravity 


Asbestos 2.8 

Asphaltum 1.4 

Borax 1.75 

Brick,  common 1.8 

Brick,  fire 2.3 

Brick,  hard 2.0 

Brick,  pressed 2.15 

Brickwork,  in  motor 1.6 

Brickwork,  in  cement 1.8 

Cement,  Portland 3.1 

Chalk 2.6 

Charcoal 0.4 

Coal,  anthracite 1.5 

Coal,  bituminous 1.27 

Concrete 2.2 

Earth,  loose 1.2 

Earth,  rammed 1.6 

Emery 4.0 

Glass 2.6 

Granite 2.65 

Gravel 1.75 

Gypsum 2.2 

Ice 0.9 

Ivory '. 1.85 

Limestone 2.6 

Marble 2.7 

Masonry 2.4 

Mica 2.8 

Mortar 1.5 

Phosphorus (         1.8 

Plaster  of  Paris 1.8 

Quartz 2.6 

Salt,  common 2.1 

Sand,  dry 1.6 

Sand,  wet 2.0 

Sandstone 2.3 

Slate 2.8 

Soapstone  2.7 

Soil,  common  black 2.0 

Sulphur 2.0 

Trap 3.0 

Tile 1.8 


170 


THE       STARRETT       BOOK 


Table  15 

Specific  Gravity  of  Gases 

(At  32  degrees  F.) 


Gas 

Sp. 
Gr. 

Gas 

.§?: 

Air. 

1.000 

Hydrogen  .  . 

0.069 

Acetylene  . 

0.910 

Illuminating  gas  .    .  . 

0.040 

Alcohol  vapor  

1.601 

Mercury  vapor  

6.940 

Ammonia  

0.592 

Marsh  gas  

0.555 

Carbon  dioxide  

1.520 

Nitrogen  

0.971 

Carbon  monoxide 

0.967 

Nitric  oxide 

1.039 

Chlorine 

2.423 

Nitrous  oxide  . 

1.527 

Ether  vapor 

2.586 

Oxygen  

1.106 

Ethylene  
Hydrofluoric  acid  
Hydrochloric  acid  

0.967 
2.370 
1.261 

Sulphur  dioxide  
Water  vapor  

2.250 
0.623 

1  cubic  foot  of  air  at  32  degrees  F.  and  atmospheric  pressure  weighs  0.0807  pound 

Table  16 
Specific  Gravity  of  Liquids 


Liquid 

fe 

Liquid 

Sp. 
Gr. 

Acetic  acid 

1.06 

Muriatic  acid 

1.20 

Alcohol,  commercial 

0.83 

Naphtha 

0.76 

Alcohol,  pure  . 

0.79 

Nitric  acid   . 

1.22 

Ammonia  

0.89 

Olive  oil  

0.92 

Benzine  
Bromine  

0.69 
2.97 

Palm  oil  
Petroleum  oil  

0.97 
0.82 

Carbolic  acid 

096 

Phosphoric  acid 

1.56 

Carbon  disulphide 

1.26 

Rape  oil 

0.92 

Cotton-seed  oil 

0.93 

Sulphuric  acid 

1.84 

Ether,  sulphuric 

0.72 

Tar  ...                   

1.00 

Fluoric  acid  
Gasoline  
Kerosene  

1.50 
0.90 
0.80 

Turpentine  oil  
Vinegar  
Water  

0.87 
1.08 
1.00 

Linseed  oil 

0.94 

Water,  sea 

1.03 

Mineral  oil 

0.92 

Whale  oil  

0.92 

171 


THE        STARRETT        BOOK 


Table  17 
Composition  of  Miscellaneous  Alloys 


Alloys 

Antimony 

Bismuth 

1 

| 

I 

1 

c 
H 

H 

N 

Brass,  common  yellow 

61.6 

2.9 

0.2 

35.3 

Brass,  to  be  rolled 

32 

1.5 

10 

Brass  castings,  common 

20 

2.5 

1.25 

Gun  metal 

8 

1 

Copper  flanges 

9 

026 

1 

Bronze  Statuary 

91.4 

1.37 

1.7 

5.53 

German  Silver 

2 

6.5 

7.9 

6.3 

Britannia  metal 

50 

25 

25 

Chinese  white  copper 

20.2 

15.8 

1.3 

12.7 

Pattern  letters 

15 

15 

70 

Bell  metal 

4 

1 

Chinese  gongs 

40.5 

9.2 

White  metal,  ordinary 

28.4 

3.7 

14.2 

3.7 

Spelter 

1 

1 

Type  metal 

1 

3-7 

172 


THE       STARR    ETT       ROOK 


Table  18 
Average  Specific  Heats  of  Various  Substances 


Substance 

Specific 
Heat 

Substance 

Specific 
Heat 

Alcohol  (absolute) 

0  700 

0  500 

Alcohol  (density  0.8)  

0.622 
0214 

Lead....  
Limestone 

0.031 
0  217 

Antimony  
Benzine 

0.051 
0  450 

Magnesia  
Marble 

0.222 
0  210 

Brass  

0.094 

Masonry,  brick  

0200 

Brickwork  

0.200 
0057 

Mercury  
Naphtha 

0.033 
0  310 

Charcoal  
Chalk 

0.200 
0215 

Nickel  
Oil  machine 

0.109 
0400 

Coal  

0.240 

Oil,  olive  

0350 

Coke  
Copper  32°  to  212°  F 

0.203 
0094 

Phosphorus  
Platinum 

0.189 
0  032 

Copper,  32°  to  572°  F  

0.101 

Quartz  ,  

0  188 

Corundum  

0198 

Sand  

0  195 

Ether 

0503 

Silica 

0  191 

Fusel  oil  
Glass      

0.564 
0  194 

Silver  
Soda 

0.056 
0231 

Gold  

0.031 

Steel,  mild  

0  116 

Graphite  

0201 

Steel  high  carbon       .       ... 

0  117 

Ice 

0504 

Stone  (generally) 

0200 

Iron,  cast  

0.130 

Sulphur  

0  178 

Iron  wrought,  32°  to  212°  F  . 

0  110 

Sulphuric  acid  .... 

0330 

32°  to  392°  F 

0  115 

Tin 

0056 

32°  to  572°  F  

0.122 

Turpentine  

0472 

32°  to  662°  F 

0  126 

Water  ... 

1  000 

Iron,  at  high  temperatures  : 

Wood,  fir  

0650 

1382°  to  1832°  F  
1750°  to  1840°  F 

0.213 
0218 

Wood,  oak  
Wood  pine 

0.570 
0467 

1920°  to  2190°  F  

0.199 

Zinc  

0.095 

173 


THE       STARRETT       BOOK 


Table  19 

Templets  for  Drilling  Standard  and  Low  Pressure  Flanged 
Valves  and  Fittings  —  American  Standard 


V 

N 

to 

*l 

§  « 

s= 

Thickness 
of  Flange 

Diam.  of 
Bolt  Circle 

"SI2 

|2 

"S« 

I§ 

0 

c^ 

S| 

II 

5^ 

Thickness 
of  Flange 

Diam.  of 
Bolt  Circle 

o« 

l§ 

0.2 

Va 
&& 

1 

4 

7A« 

3 

4 

H« 

42 

53 

2% 

49H 

36 

VA 

1% 

4^ 

H 

3H 

4 

7/ie 

44 

55% 

2% 

51% 

40 

IX 

1H 

5 

%6 

SK 

4 

*Ji 

46 

57% 

2^6 

53% 

40 

1«A 

2 

6 

M 

4% 

4 

M 

48 

59H 

2% 

56 

44 

15A 

2H 

7 

^6 

SM 

4 

K 

50 

61% 

2% 

58% 

44 

1% 

3 

7H 

M 

6 

4 

H 

52 

64 

2K 

60H 

44 

1% 

3H 

8H 

15ft6 

7 

4 

5^ 

54 

66% 

3 

62% 

44 

1% 

4 

9 

15Ae 

7^ 

8 

H 

56 

68% 

3 

65 

48 

1% 

4^ 

9% 

!%6 

7% 

8 

% 

58 

71 

3H 

67% 

48 

1% 

5 

10 

!%6 

8M 

8 

% 

60 

73 

3K 

69% 

52 

1% 

6 

11 

i 

9H 

8 

% 

62 

75% 

3% 

71% 

52 

IH 

7 

12  H 

l^le 

10% 

8 

% 

64 

78 

3% 

74 

52 

IH 

8 

13  M 

m 

11% 

8 

% 

66 

80 

m 

76 

52 

1% 

9 

15 

1% 

13% 

12 

% 

68 

82% 

VA 

78% 

56 

IK 

10 

16 

1%6 

14% 

12 

K 

70 

84^ 

m 

80^ 

56 

IK 

12 

19 

Hi 

17 

12 

J^ 

72 

86H 

3M 

82^ 

60 

IK 

14 

21 

iH 

18% 

12 

l 

74 

S81A 

3H 

84^ 

60 

IK 

15 

22^ 

IK 

20 

16 

l 

76 

90% 

m 

86H 

60 

IK 

16 

23^ 

l%a 

21% 

16 

1 

78 

93 

3% 

88% 

60 

2 

18 

25 

l»Ae 

22% 

16 

1H 

80 

95% 

3% 

91 

60 

2 

20 

27H 

1^6 

25 

20 

1H 

82 

97H 

3K 

93% 

60 

2 

22 

293^ 

l18Ae 

27% 

20 

1% 

84 

99% 

3Ji 

95H 

64 

2 

24 

32 

IK 

29H 

20 

1% 

86 

102 

4 

97% 

64 

2 

26 

34% 

2 

31% 

24 

1% 

88 

104% 

4 

100 

68 

2 

28 

36^ 

2^6 

34 

28 

1% 

90 

106^ 

4^ 

102% 

68 

2K 

30 

38% 

2K 

36 

28 

1% 

92 

108% 

4H 

104^ 

68 

2K 

32 

41% 

2% 

38>i 

28 

1H 

94 

111 

4% 

106% 

68 

2K 

34 

43% 

2%6 

40^ 

32 

1H 

96 

113% 

4% 

108^ 

68 

2% 

36 

46 

2K 

42% 

32 

1H 

98 

115H 

4M 

110% 

68 

2% 

38 

48% 

2K 

45% 

32 

1H 

100 

117% 

4M 

113 

68 

2% 

4.0 

CAS./ 

?V4 

47  \£ 

36 

154 

4U 

OU/4 

^/2 

**(  74 

A/  8 

Bolt  holes  are  drilled  K  inch  larger  than  nominal  diameter  of  bolts. 
174 


THE        STARRETT       BOOK 


Table  20 

Templets  for  Drilling  Extra  Heavy  Flanged  Valves  and 
Fittings — American  Standard 


Size 

•  Diam.  of 
Flange 

Thickness 
of  Flange 

Diam.  of 
Bolt  Circle 

No.  of 
Bolts 

Size  of 
Bolts 

1 

4^ 

>#« 

3K 

4 

H 

in 

5 

% 

3% 

4 

/4 

6 

13/16 

4 

% 

2  2 

6M 

I/fa 

5  2 

4 

5/8 

2^ 

71^ 

1 

57^ 

4 

3 

8K 

1/^8 

6^ 

8 

% 

3/^ 

9 

18/16 

7K 

8 

% 

4 

10 

IK 

7% 

8 

% 

4/^ 

103^ 

15/16 

8 

% 

5 

11 

9K 

8 

% 

6 

12H 

17/16 

10^ 

12 

% 

7 
8 

14 
15 

3H 

13  8 

12 
12 

7/8 

7A 

9 

16K 

¥ 

14 

12 

10 

17J^ 

15K 

16 

1 

12 

20^ 

2  8 

17% 

16 

l/^ 

14 

23 

2/'8 

20K 

20 

1^8 

15 

24^ 

2%6 

21/^ 

20 

IK 

16 

25^ 

2K 

22^ 

20 

IK 

18 

28 

2^i 

24% 

24 

IK 

20 

30^ 

2^ 

27 

24 

if! 

22 

33 

2/^ 

29K 

24 

24 

36 

2% 

32 

24 

i/^ 

26 

38K 

34^ 

28 

i/^ 

28 

40% 

2^5/16 

37 

28 

i/^ 

30 

43 

3 

39  K 

.  28 

1% 

32 

45K 

33^8 

41^ 

28 

1/^8 

34 

47^ 

3K 

43^ 

28 

1J/8 

36 

50 

3^g 

46 

32 

IJ/g 

38 

52K 

3^16 

48 

32 

1% 

40 

54^ 

3%6 

50K 

36 

l/^ 

42 

57 

31^io 

52% 

36 

\1/o 

44 

59K 

3% 

55 

36 

2 

46 

61^ 

3% 

57K 

40 

2 

48 

65 

60% 

40 

2 

Bolt  holes  are  drilled 


inch  larger  than  nominal  diameter  of  bolts. 
175 


THE       S    T    A    R    RETT       BOOK 


Table  21  — Tap  Drills 

For  A.  S.  M.  E.  Standard  and  .Special 

Machine  Screw  Taps 

The  diameter  given  for  each  hole  to  be  tapped  allows  for  a 
practical  clearance  at  the  root  of  the  thread  of  the  screw  and  will 
not  impose  undue  strain  upon  the  tap  in  service. 


Size 
of  Tap 

No.  of 
Threads 

Size  of 
Drill 

Size  of 
Tap 

No.  of 
Threads 

Size  of 
Drill 

0 

80 

.0465 

9 

32 

.1405 

1 

64 

.055 

10 

24 

.140 

1 

72 

.0595 

10 

30 

.152 

2 

56 

.0670 

10 

32 

.154 

2 

64 

.070 

12 

24 

.166 

3 

48 

.076 

12 

28 

.173 

3 

56 

.0785 

14 

20 

.182 

4 

36 

.080 

14 

24 

.1935 

4 

40 

.082 

16 

20 

.209 

4 

48 

.089 

16 

22 

.213 

5 

36 

.0935 

18 

18 

.228 

5 

40 

.098 

18 

20 

.234 

5 

44 

.0995 

20 

18 

.257 

6 

32 

.1015 

20 

20 

.261 

6 

36 

.1065 

22 

16 

.272 

.6 

40 

.110 

22 

18 

.281 

7 

30 

.113 

24 

16 

.295 

7 

32 

.116 

24 

18 

.302 

7 

36 

.120 

26 

14 

.316 

8 

30 

.1285 

26 

16 

.323 

8 

32 

.1285 

28 

14 

.339 

8 

36 

.136 

28 

16 

.348 

9 

24 

.1285 

30 

14 

.368 

9 

30 

.136 

30 

16 

.377 

NOTE  :  —  Special  Taps  are  in  Bold  Face  Type. 
176 


THE       STARRETT       BOOK 


Table  22  — Tap  Drills  for  Machine  Screws 


Size  of 
Tap 

American 
Standard 
Diameter  in 
Inches 

Size  of  Drill 
for  Outside 
Diameter  of 
Screw 

Size  of  Drill 
for  Tapping 
Hole 

Size  of 
Tap 

American 
Standard 
Diameter  in 
Inches 

Size  of  Drill 
for  Outside 
Diameter  of 
Screw 

°H| 

2x48) 

50 

13x20) 

17 

2x56 

.25763 

44 

49 

13x22     • 

.071961 

*%4 

17 

2x64] 

48 

13x24] 

15 

3x40) 

49 

14x20) 

15 

3x48 

.22942 

39 

47 

14  x  22 

.064084 

V* 

11 

3x56] 

45 

14x24] 

10 

4x32) 

46 

15x18) 

12 

4x36 
4x40] 

.20431 

33 

44 
43 

15  x  20 
15  x  22 

.057068 

F 

10 

8 

15x24] 

7 

5x30) 
5x32 
5x36 
5x40] 

.18194 

tt 

43 
42 
41 
38 

16x16) 
16  x  18 
16x20] 

.05082 

I 

12 

7 

6x30) 
6  x  32 
6  x  36 

.16202 

28 

38 
37 
36 

17x16) 
17  x  18 
17x20j 

.045257 

L 

8 
4 
3 

6x40J 

35 

18x16) 

2 

7x28) 
7x30 

.14428 

24 

34 
33 

18  x  18 
18x20] 

.040303 

19/64 

2 
1 

7x32] 

32 

19x16) 

1 

8x24) 
8x30 

.12849 

19 

31 
31 

19  x  18 
19x20] 

.03589 

*; 

B 

8x32] 

30 

20x16) 

c 

9x24 
9x28 
9x30 
9x32 

.11443 

16 

30 
28 
28 
26 

20  x  18 
20x20] 

22  x  16  \ 
22  x  18  / 

.031961 
.025347 

p 

s 

E 

F 

H 

10x24) 

26 

24  x  14  ) 

L 

10  x  30 
10x32] 

.10189 

11 

24 
24 

24  x  16 
24x18] 

.0201 

% 

M 
N 

11x24) 
11  x  28 

.090742 

6 

21 
20 

26  x  14  \ 

26  x  16  / 

.01594 

18/82 

0 
p 

11x30] 

19  ' 

12x20 

24 

28  x  14  \ 

28  x  16  / 

.012641 

fti 

R 

12x22 

20 

12x24 

.080808 

%2 

19 

30  x  14  \ 

u 

12x28 

18 

30  x  16  / 

.010025 

2%4 

V 

177 


INDEX 

Abbreviations  for  Drawings 12 

Abrasives,    Grain .    ,    .    .  43 

Adjusting  Toolmakers'  Buttons  with  Micrometer   .     .  104 

Algebraic  Signs 132-136 

Aligning  Shafting 119 

Alloys,  Composition  of , 172 

Angle,  Measurement  of 140 

Bench   Work 35 

Bolt  and  Screw  Lists     .    .- 7 

Boring  Holes  in  Jig  Body 103 

Buttons'  Toolmakers' 104 

Calipering  over  a  Flange 27 

Calipers,  for  Testing  Screw  Threads 85 

Calipers,   Hermaphrodite 69 

Calipers,  Inside  and  Outside 27 

Calipers,  Micrometer 19 

Calipers,    Spring 26 

Calipers,  Vernier 16 

Carbon  Steel 75 

Carbon  Steel  Drills,  Speed  of 51 

Center  Gage 67 

Center  Punches 56 

Change  Gears 79 

Chipping 38 

Chisels  for  Chipping 38 

Chucking 93 

Chucking  Tools : 96 

Coefficient  (Algebra) 127 

Composition  of  Alloys 172 

Compound  Gears  for  Thread  Cutting • 82 

Contact  Measuring 15 

Counterboring : 62 

Cup   Wheels 117 

Cutting  Compounds  for  Drills 53 

Cutting  Lips  of  Drills 47 

Cutting  Screw  Threads 77 

Deep  Hole  Drilling .  02 

Detail  Drawings 7 

Dividers,  Spring 28 

Draw  Filing 42 

Drawing  the  Drill 55 

Drill  Grinding  . 48 

Drill  Speed    .        51 

Drilling 48 

Drilling  Deep  Holes 62 

Drilling,  Drawing  the  Drill  .    .    .    .  ' 55 

Drilling  for  Reamer "...  57 

Drilling  for  Tapping 58 

Drilling,  Holding  Work 56 

Drilling  Large  Holes 61 

Drilling,  Starting  Drill 55 

Drilling,  Templets  for  Extra  Heavy  Flanged  Valves  and  Fittings  .  1J5 

178 


THE        STARRETT        BOOK 

Drilling,  Templets  for  Standard  and  Low  Pressure  Flanged  Valves 

and  Fittings 174 

Drills,  Cutting  Compounds 53 

Drills,  Cutting  Lips 47 

Drills,  Kinds 47 

Drills,  Letter  Sizes  of 59 

Drills,  Making ' 97 

Drills,  Testing  Cutting  Lips 49 

Eccentric  Turning 91 

Elementary  Algebra 126 

Emery,  Grades  of 43 

Equations 134 

Equivalent  Tables 60 

Expansion  of  Metals 169 

Exponent 127 

Extra  Heavy  Flanged  Valves  and  Fittings,  Templets  for  Drilling  .  175 

Files,  Kinds  .  40 

Filing 40 

Filing,  Testing  Surface 42 

Fits,  Amounts  to  Leave 30 

Flanged  Fittings,  Templets  for  Drilling  .    .    . 174 

Forced  Fits 29 

Forces 151 

Gear  Speeds,  Formulas  for 165 

Gears  for  Thread  Cutting 79 

Gears,  Speed  of 163 

Gears,  Trains 165 

Grades  of  Emery 43 

Grading  Grinding  Wheels Ill 

Grinding 109 

Grinding,  Allowances  for 110 

Grinding,  Amounts  to  leave 113 

Grinding  Cylindrical 113 

Grinding  Flat  Surfaces 116 

Grinding  Wheels,  Grade  and  Grain 115 

Grinding,  Measuring  Work 116 

Grinding  Milling  Cutters 100 

Grinding  Speeds  for 114 

Grinding  Wheels 109,  111 

Grinding  Wheels,  Grades Ill 

Grinding  Wheels,  Mounting 116 

Hack  Saw  Machine 45 

Hack   Saws 43 

Hack  Saws,  Cutting  Speed 44 

Hack  Saws,  What  One  to  Use  . 46 

Hand  Chipping 38 

Height  Gage 17 

High  Speed  Steel  Drills,  Speed  of 51 

Holding  Drill  in  Spindle 56 

Holding  Work  for  Drilling 57 

Holding  Work  in  Chucks 95 

How  to  Read  a  Micrometer 21 

How  to  Read  a  Vernier 22 

How  to  Read  a  Vernier  Micrometer .  23 

Involute 146 

179 


THE        STARRETT       BOOK 

Jig  Bushings 107 

Jig  for  Drilling  Cylinder  Flange 108 

Jigs  and  Fixtures 101 

Jigs,  Locating  Bushing  Holes 102 

Jigs,  Types 101 

Knurling '..... 96 

Lapping 117 

Lathe 65 

Lathe  Centers 65 

Lathe  Gearing 106 

Lathe  Tools 70,  75 

Lathe  Tools,  Clearance 72 

Lathe  Tools,  Grinding 73 

Lathe  Tools,  Rake 72 

Lathe  Tools,  Setting 73 

Lathe  Tools,  Testing  Cutting  Angles 74 

Lathe  Work,  Measuring 85 

Laying  Out  for  Drilling 53 

Length  of  Belts,  Formulas  for 161,  162 

Level  for  Aligning  Shafting 119 

Leveling  Instrument 119 

Leveling  Instrument,  How  to  Set  Up 124 

Levels,  Finding  Difference 125 

Levers 153 

Limits  of  Accuracy , 29, 32 

Locating  Bushing  Holes  in  Jigs 102 

Locating  Jig  on  Face  Plate 103 

Locating  Machinery 123 

Low  Pressure  Flanged  Fittings 174 

Lubricant  for  Thread  Cutting 84 

Mandrels,  Use  of 76 

Measuring  Lathe  Work 85 

Measuring  Screw  Threads 84 

Measuring  Tools 13 

Measuring  Work,  Grinding 116 

Mechanics 151 

Melting  Point  of  Metals 169 

Mensuration 140 

Micrometer,  Adjusting  Buttons  with 104 

Micrometer  as  a  Gage 25 

Micrometer  Calipers 19 

Micrometer,  for  Measuring  Screw  Threads 86 

Micrometer,  How  to  Read 21 

Micrometers,  Adjustment  for  Wear 25 

Micrometers,  Quick  Adjustment  .    .  • 25 

Milling  Cutters 99 

Milling  Cutters,  Grinding 100 

Plane  Figures 142,  146 

Plate  for  Laying  Out 37 

Plumb  Bobs 121 

Polishing 43 

Preparing  Surface  for  Laying  Out 35 

Protractors 37 

Pulley  Diameters  and  Speeds,  Formulas  for 157 

Pulleys       155 

180 


THE        STARRETT       BOOK 

Pulleys,  or  Blocks   .    . 154 

Quick  Adjustment  of  Micrometers 25 

Radical  Sign 128 

Reamers,  Making 97 

Screw    Threads 77 

Screw  Threads,  Measuring ." 84 

Screw  Threads,  Pitch 77 

Screw  Threads,  Properties  of  U.  S.  Standard 78 

Scribing  Lines  for  Laying  Out 35 

Section  Lines 11 

Shop  and  Engineering  Formulas 137 

Signs  (Algebra) 132 

Sliding  Pit   . 29 

Solids 146 

Specific  Gravity  of  Gases 171 

Specific  Gravity  of  Liquids .    ' 171 

Specific  Gravity  of  Metals 1G9 

Specific  Gravity  of  Substances 170 

Specific  Heat  of  Substances 173 

Speed  of  Drills 52 

Speed  of  Gears,  Formulas  for 165 

Standard  Flanged  Fittings 174 

Starting  Drill 55 

Stellite 76 

Surface  Plates 38- 

Table  1    Allowances  for  Different  Classes  of  Fits 31 

2  Speeds  and  Feeds  for  Drilling 51 

3  Speed  of  Drills 52 

4  Letter  Sizes  of  Drills 59 

5  Sizes  of  Tap  Drills •  59 

6  TJ.  S.  Standard  Screw  Threads 78 

7  Brown  &  Sharpe  Taper  Shanks 87 

8  Morse  Taper  Shanks 88 

9  Tapers 92 

10  Allowances  for  Grinding     . 110 

11  Grinding  Wheel  Speeds 114 

12  Grinding  Wheels  for  Different  Materials 115 

13  Specific  Gravity  and  Properties  of  Metals 169 

14  Specific  Gravity  of  Substances 170 

15  Specific  Gravity  of  Gases 171 

16  Specific  Gravity  of  Liquids 171 

17  Composition  of  Alloys 172 

18  Specific  Heat  of  Substances 173 

19  Templets  for  Drilling  Standard  and  Low  Pressure  Flanged 

Valves  and  Fittings  —  American  Standard 174 

20  Templets  for  Drilling  Extra  Heavy  Flanged  Valves  and 

Fittings  —  American  Standard 175 

21  Tap  Drills,  A.S.M.E.  Standard .    .    .  176 

22  Tap  Drills  for  Machine  Screws 177 

Tap  Drills,  Sizes  of   ...    t 59,  78,  176,  177 

Taper  in  Given  Length 90 

Taper  Shanks 87,  88 

Taper  Turning 86 

Taper  Turning,  Offset  of  Centers,  Amount 90 

Tapers,  Testing 91 

181 


THE        STARRETT        BOOK 

Targets 123 

Testing  Cutting  Lips  of  Drills 4!) 

Testing  Flat  Filing 42 

Test  Indicator      .    .    .    .   • 67 

Testing  Turned  Taper 91 

Thread  Tool,  Form  of 82 

Thread  Tool,  Setting 84 

Tolerance,  Limits  of 32 

Tool  Holders 75 

Tool  Making 97 

Toolmakers'  Buttons 103 

Train  of  Gears 165 

Transferring  Measurements 26 

Truing  Work  in  Chucks 95 

Turning,  Work  Centers 69 

Universal  Dial  Test  Indicator 07,  103 

Vernier  Calipers  .    .    .    .- 16 

Vernier  Height  Gage 17.  10r> 

Vernier,  How  to  Read 22 

Vernier  Micrometer,  How  to  Read 23 

Vitrified  Wheels 109 

Wear  of  Micrometers 25 

Weight  per  Cuhic  Foot  of  Substances 170 


What  Hack  Saw  to  Use 

Windlass 

Work  Centers 

Work  Centers,  Locating  ,  -  , 
Working  Drawing  Abbreviations 
Working  Drawings 


46 
154 
69 
89 
12 


182 


THE        STARR    E    T    T       BO    Q    K 

SETS  OF  TOOLS 

FOR  APPRENTICES  AND  STUDENTS 

SET   NO.  900 

IN  FOLDING  LEATHER  CASE 

Size  of  case  folded,  7"  x  4%"  x  l%* 


Set  No.  900  consists  of  the  leather  case  and  the 
following  tools: 

No.    11,  6"  Combination  Square,  com-  No.  390,  Center  Gage 

plete  No.  241,  4"  Caliper 

No.  117B,  Center  Punch  No.  79, 4"  Outside  Caliper  with  solid  nut 

No.  321, 6"  Flexible  Steel  Rule  in  pocket  No.  73,  4"  Inside  Caliper  with  solid  nut 

case  No.  83,  4"  Divider  with  solid  nut 


PRICE,  set  complete 


$6.00 


183 


THE        STARRETT       BOOK 


SETS  OF  TOOLS 

FOR  APPRENTICES  AND  STUDENTS 

SET  NO.  901 

IN  NICELY  FINISHED  WOODEN  CASE 

Size  of  case,  12"x7"xl^ 


Set  No.  901  consists  of  the  wooden  case  and  the 
following  tools: 


No.  11,  6"  Combination  Square,  com- 
plete 

No.  321,  6"  Flexible  Steel  Rule  in 
pocket  case 

No.  117B,  Center  Punch 

PRICE,  set  complete 


No.  390,  Center  Gage 

No.  77,  5"  Divider  with  solid  nut 

No.  79, 6"  Outside  Caliper  with  solid  nut 

No.  73,  6"  Inside  Caliper  with  solid  nut 


$6.15 


184 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


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.RY  U>E 

i  • 


Due  end  of  WINTER  Quarter    MAB  1  5  9flQ  3  * 
subject  to  redall  after- 

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